Find the value of c such that the expression is a​ perfect-square trinomial.
k^2 -3k+c
k^2 -3k+c=k^2 -3k+__ ​(Type an integer or a simplified​ fraction.)

Answer:

-3

Step-by-step explanation:

To find the slope (m) of the line that passes through Point A(3, -9) and the origin (0, 0), we can use the formula:m = rise/run = (change in y)/(change in x)We can calculate the change in y and change in x as follows:

Change in y = y2 - y1 = 0 - (-9) = 9

Change in x = x2 - x1 = 0 - 3 = -3

Substituting these values into the formula, we get:

m = rise/run = 9/-3 = -3

Therefore, the slope of the line that passes through Point A(3, -9) and the origin is -3.

The total area of the figure with of the semicircle and triangle is 12.27 sq. ft.

Half of a circle is known as a semicircle, and the diameter of the circle is equal to the length of the semicircle's straight edge. A sector of a circle is a section of a circle that is bounded by an arc, two radii, and both. A semicircle is always half of a circle and has a constant central angle of 180 degrees, but a sector can be any part of a circle and has a central angle that can vary from 0 to 360 degrees. This is the major distinction between the two.

Given, the diameter of the semicircle is 3 ft, so its radius is 1.5 ft.

Now, area of the semicircle is given as:

A = 1/2 * pi * (1.5)² = 1.77 sq ft

The area of the triangle is:

A = 1/2 * 3 ft * 7 ft = 10.5 sq ft

Adding the areas we have the total area of the figure:

1.77 sq ft + 10.5 sq ft = 12.27 sq ft

Hence, the total area of the figure is 12.27 sq. ft.

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Answer:

11 1/2

Step-by-step explanation:

(a) The probability that the sum of the numbers is 8 is 0.1.

(b) The probability that the sum of the number is 6 or less is 0.5.

(c) The probability that the first number is 2 or the sum is 5 is 0.35.

A probability is the number of desired outcomes divided by the number of total outcomes.

The possible outcomes are:

(1,2), (1,3), (1,4), (1,5).

(2,1), (2,3), (2,4), (2,5).

(3,1), (3,2), (3,4), (3,5).

(4,1), (4,2), (4,3), (4,5).

(5,1), (5,2), (5,3), (5,4).

Total outcomes = 20

(a) The sum of the numbers is 8.

There are only two ways to get a sum of 8: (3, 5), (5,3). So the probability of getting a sum of 8 is:

P(sum of 8) = 2/20

= 0.1

Therefore, the required probability is 0.1.

(b) The sum of the number is 6 or less.

To get a sum of 6 or less, we can have the following combinations:(1, 2), (1, 3), (1, 4), (1, 5), (2,1), (2, 3), (2,4), (3,1), (3,2), (4,1), (4,2), (5,1).So the probability of getting a sum of 6 or less is:

Total outcomes = 20

P(sum of 6 or less) = 10/20

=0.5

Therefore, the required probability is 0.5.

(c) The first number is 2 or the sum is 5

There are three ways to satisfy this condition:(2,1), (2, 3), (2,4), (2, 5), (1,4), (3, 2), (4,1). So the probability of getting a number that satisfies this condition is:

Total outcomes = 20

P(first number is 2 or sum is 5) = 7/20

= 0.35.

Therefore, the required probability is 0.35.

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The best center of the speed of the last 10 pitches thrown by a pitcher is the mean

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

{90, 92, 85, 88, 94, 86, 93, 90, 88, 95}

The possible measure of centers are

In this case, we use the mean

This is because the data values do not have any outlier present in them

Hence, the center is the mean

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The size and nature of the dataset, the choice of independent variables, and the assumptions underlying the model, should also be considered when interpreting [tex]R^2[/tex] values.

The percent of the total variance that can be explained by the regression equation is known as the coefficient of determination, denoted as[tex]R^2.[/tex]

It represents the proportion of the total variation in the dependent variable (Y) that is accounted for by the independent variable(s) (X) included in the regression model.
To calculate[tex]R^2[/tex], you can follow these steps:
Obtain the sum of the squared differences between the actual and predicted values of the dependent variable (also known as the residual sum of squares, or RSS).
Obtain the sum of the squared differences between the actual values of the dependent variable and their mean (also known as the total sum of squares, or TSS).
Divide the RSS by the TSS: [tex]R^2 = 1 - (RSS/TSS).[/tex]
[tex]R^2[/tex] ranges between 0 and 1, with higher values indicating a better fit of the regression model.

An[tex]R^2[/tex] of 1 indicates that the regression equation perfectly explains the total variance, while an [tex]R^2[/tex] of 0 indicates that the regression equation does not explain any of the total variance.
Keep in mind that while[tex]R^2[/tex] is a useful measure of model fit, it should not be the only criterion used to evaluate the quality of a regression model.

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1) The name of the shape is rectangle

2) The name of the shape is trapezoid

3) The name of the shape is rhombus

4) The name of the shape is rectangle

From the question, we are to state the most specific name for each of the given figures

1.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

2.

We have a quadrilateral

Only a pair of opposite sides are parallel

The name of the shape is trapezoid

3.

We have a quadrilateral

Opposite sides are parallel and equal

All sides are equal

None of the angle is a right angle

The name of the shape is rhombus

4.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

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Hong rode the scooter for approximately 86 minutes.

Let's start by using algebra to solve for the number of minutes Hong rode the scooter.

Let's say the number of minutes Hong rode the scooter is "m". Then, we can set up the following equation:

Total cost = $5 fee + 9 cents per minute x m minutes

$12.74 = $5 + $0.09m

Next, we'll solve for "m" by isolating it on one side of the equation:

$12.74 - $5 = $0.09m

$7.74 = $0.09m

m = $7.74 ÷ $0.09

m ≈ 86

Therefore, Hong rode the scooter for approximately 86 minutes.

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Answer:

Step-by-step explanation:

Here you go:

64 = 512x - 4

64 + 4 = 512x - 4 + 4

68 = 512x

Hope this helps

The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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Answer: D

Step-by-step explanation:

Zach won because 3 16/24 is less than 3 15/24. Then, 3.666666 is less than 3.625

Yes, 2 is a zero of the polynomial  [tex]Xe3-8xe2+18x-12[/tex]

To determine if 2 is a zero of the polynomial [tex]Xe3-8xe2+18x-12[/tex], we can plug in 2 for x and see if the result is 0.

So, if we substitute x=2, we get:

[tex](2)^3 - 8(2)^2 + 18(2) - 12 = 0[/tex]

Simplifying this equation, we get:

8 - 32 + 36 - 12 = 0

This equation is true, which means that 2 is indeed a zero of the polynomial [tex]Xe3-8xe2+18x-12.[/tex]

Therefore, we can conclude that the polynomial can be factored as:

[tex](X-2)(X^2-6X+6)[/tex]

This means that the other two zeros of the polynomial are the solutions of the quadratic equation [tex]X^2-6X+6=0[/tex] which can be found using the quadratic formula.

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Answer:

f(x) is the blue graph, g(x) is the red graph.

x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2

16 - x^2 = 0 when x = -4, 4

So the area between these two graphs is (using the TI-83 graphing calculator):

fnInt (16 - x^2, x, -4, 4) = 85 1/3

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)=4\implies 2^{\log_2(16x)}=2^4\implies 16x=2^4\implies x=\cfrac{2^4}{16}\implies x=1[/tex]

Therefore, the value of x that makes the equation true is x = 2/3.

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It typically consists of variables, constants, and mathematical operators (such as addition, subtraction, multiplication, and division) that are used to describe a relationship between two or more quantities. Equations are often used in various fields of mathematics, science, engineering, and economics to model real-world phenomena and solve problems.

The equation is:

[tex]x + 4 = 4x + 2[/tex]

We need to find the value of x that makes this equation true.

First, we can simplify the equation by subtracting x from both sides:

[tex]4 = 3x + 2[/tex]

Next, we can simplify further by subtracting 2 from both sides:

[tex]2 = 3x[/tex]

Finally, we can solve for x by dividing both sides by 3:

[tex]x = 2/3[/tex]

Therefore, the value of x that makes the equation true is x = 2/3.

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The expression that gives the area as a function of the width is 4w²+3w.( option B)

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of a rectangle is expressed as ;

A = l×w, where l is the length and w is the width.

Since the length is 3 inches more than four times the width, then;

l = 3+4w

Representing 3+w for l in the area formula, then we have;

A = (3+4w)(w)

A = 4w²+3w

therefore the expression that represents the area is 4w²+3w

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The slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

The slope of the linear regression prediction equation can be calculated by using the formula:

slope = (y2 - y1) / (x2 - x1)

where y2 is the second data point (in this case, 28,600),

y1 is the first data point (in this case, 27,000),

x2 is the second value of the independent variable (in this case, 13 years of schooling), and

x1 is the first value of the independent variable (in this case, 12 years of schooling).

Plugging in the values, we get:

slope = (28,600 - 27,000) / (13 - 12)

slope = 1,600 / 1

slope = 1,600

Therefore, the slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

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Answer:

6x² + 19x + 15

Step-by-step explanation:

(2x+3)(3x + 5)

= 6x² + 10x + 9x + 15

= 6x² + 19x + 15

So, the answer is 6x² + 19x + 15

The second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve.

To find the leftmost point on the curve defined by the parametric equations x = t² + 2t and y = t² - 2t + 3, we need to find the value of t that corresponds to this point. We can do this by analyzing the derivative of the curve with respect to t.

The leftmost point on the curve corresponds to the point where the slope of the curve is zero or undefined. This occurs when the derivative of y with respect to x is zero or undefined.

We can express y as a function of x by eliminating t from the given parametric equations. Solving for t in terms of x, we get:

t = -1 ± √(x + 1)

Substituting this value of t in the equation for y, we get:

y = (x + 1) ± 4√(x + 1) + 3

y = ±4√(x + 1) + x + 4

To find the leftmost point on the curve, we need to find the value of x that corresponds to this point. We can do this by finding the minimum value of x for which y is defined.

Differentiating y with respect to x, we get:

dy/dx = 1 + 2/√(x + 1)

Setting dy/dx = 0, we get:

1 + 2/√(x + 1) = 0

2/√(x + 1) = -1

Solving for x, we get:

x = 3

Note that this value of x is within the given range of -2 ≤ t ≤ 3. Therefore, the leftmost point on the curve is the point corresponding to t = 1.

To justify that we have found the requested point, we can analyze the second derivative of y with respect to x. The second derivative will tell us whether the point corresponds to a local minimum, local maximum, or inflection point.

Differentiating dy/dx with respect to x, we get:

d²y/dx² = -2/[tex](x + 1)^{(3/2)}[/tex]

Substituting x = 3, we get:

d²y/dx² = -2/64

Since the second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve. Therefore, we have found the leftmost point on the curve as requested.

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The question is -

Identify the requested point and justify that you have found the requested point by analyzing an appropriate derivative. x = t² + 2t, y = t² - 2t + 3, - 2 ≤ t ≤ 3 Leftmost point

Answer: 3 additional men are needed to reduce the work by 1 hour.

Step-by-step explanation: There is a relationship between working men and the hours needed to complete the work, both are inversely proportional to each other.

Let, x represent the number of men required to complete the work in :

5-1 = 4 hours

then,

4x = 5 * 12 = 60

Hence,

x = 60/4 = 15

There are 12 men, who are working currently on the job and 15 men are required to complete the work in 1 hour less time.

Then,

15 - 12 = 3

3 additional men are required to reduce work by 1 hour.

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For events A and B to be independent, the condition that must be true is:
P(A ∩ B) = x * y

The correct condition that must be true if events A and B are independent is:

P(A ∩ B) = P(A) x P(B).

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A ∩ B) is the probability of both events A and B occurring together.

In other words, if events A and B are independent, then the probability of both events occurring together is equal to the product of their individual probabilities.

When two events A and B are independent, the following condition must be true:
P(A ∩ B) = P(A) * P(B)
In your case, the probability of event A is x, and the probability of event B is y.

Therefore, the correct answer is:

P(A ∩ B) = x*y

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the probability that an American man is 69.8 inches or taller is 0.5 (or 50%).

To solve this problem, we can use the properties of the normal distribution and the standard normal distribution.

First, we need to standardize the variable (the height of men) to a standard normal variable (with a mean of 0 and a standard deviation of 1). We can do this using the formula:

[tex]z = (x - mu) / sigma[/tex]

where z is the standard normal variable, x is the original variable, mu is the mean of the original variable, and sigma is the standard deviation of the original variable.

In this case, we want to find the probability that an American man is 69.8 inches or taller. So we need to calculate the z-score for x = 69.8:

[tex]z = (69.8 - 69.8) / 3.5 = 0[/tex]

The z-score is 0 because 69.8 is equal to the mean of the distribution.

Next, we can use a standard normal distribution table (or a calculator with a normal distribution function) to find the probability that a standard normal variable is less than or equal to 0. We can also use the fact that the area under the standard normal curve is 1.

Using a standard normal distribution table, we find that the probability that a standard normal variable is less than or equal to 0 is 0.5.

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Answer:

x> - 15

Step-by-step explanation:

I guess this will help

Answer:

Angles 6 and 8 are vertical angles.

The distance of the base of the tower and the airplane is 348.5 ft,  and the right option is 4. 348.5 ft.

Distance is the length between two points.

To calculate the distance of the base of the tower and the airplane, we use the formula below.

Formula:

Where:

From the diagram,

Given:

SUbstitute these values into equation 1 and solve for A

Hence, the right option is 4. 348.5 ft.

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The expression that represents the total price of buying g pounds of grapes, b pounds of bananas, and p pounds of pears is Total cost = $2.19g + $0.59b + $1.49p

In this case, we need to use the given prices per pound of each fruit to calculate the total cost of purchasing a certain amount of each fruit. We can do this by multiplying the price per pound by the number of pounds of each fruit we want to buy, and then adding up these values.

So, to create the expression, we can start by using the given prices to calculate the cost of each fruit:

Grapes: $2.19/pound

Bananas: $0.59/pound

Pears: $1.49/pound

Next, we can use the variables g, b, and p to represent the number of pounds of each fruit we want to buy. We then multiply each price by its respective variable to get the cost of each type of fruit:

Cost of grapes: $2.19/g x g = $2.19g

Cost of bananas: $0.59/b x b = $0.59b

Cost of pears: $1.49/p x p = $1.49p

Finally, we can add up the costs of all three types of fruit to get the total cost:

Total cost = $2.19g + $0.59b + $1.49p

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Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.

Given statement is True.

The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.

By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.

This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.

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A. The number of 7-card stud poker hands is 133,784,560 and the number of 7-card stud poker hands is 674,274,182,400.

B. The number of hands of 7-draw poker that contain the ace of hearts is 18,009,460.

C. The probability that a 7-card draw hand contains the ace of hearts is 0.135.

a) The number of 7-card draw poker hands can be calculated using the combination formula, which is:

[tex]^{n} C_{r}[/tex] = n! / (r! * (n - r)!)

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card draw poker hands is:

[tex]^{52} C_{7}[/tex] = 52! / (7! * (52 - 7)!)

= 133,784,560.

The number of 7-card stud poker hands can be calculated using the permutation formula, which is:

[tex]^{n} P_{r}[/tex] = n! / (n - r)!

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card stud poker hands is:

[tex]^{52} P_{7}[/tex] = 52! / (52 - 7)!

= 674,274,182,400.

b) To count the number of hands of 7-draw poker that contain the ace of hearts, we can treat the ace of hearts as a special card that must be included in each hand. Then, we need to choose the remaining 6 cards from the 51 cards that are not the ace of hearts.

So, the number of hands of 7-draw poker that contain the ace of hearts is:

[tex]^{51} C_{6}[/tex] = 51! / (6! * (51 - 6)!)

= 18,009,460.

c) To calculate the probability that a 7-card draw hand contains the ace of hearts, we can use the formula:

P(event) = number of favourable outcomes / total number of possible outcomes

The total number of possible 7-card draw hands is 133,784,560, which we calculated in part (a).

The number of favourable outcomes is the number of hands of 7-draw poker that contain the ace of hearts, which we calculated in part (b).

So, the probability that a 7-card draw hand contains the ace of hearts is:

P(ace of hearts) = 18,009,460 / 133,784,560 ≈ 0.135

The required probability is 0.135.

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Answer:

To determine which ratio is proportional to 80:60, we need to simplify the ratio by dividing both terms by their greatest common factor. In this case, the greatest common factor of 80 and 60 is 20, so:

80/20 = 4

60/20 = 3

Therefore, the simplified ratio is 4:3.

Now we can compare this ratio to the given options to see which one is proportional to 4:3:

16:15 is not proportional

16:12 is proportional (since 16/4 = 4 and 12/3 = 4)

18:15 is not proportional

18:12 is proportional (since 18/3 = 6 and 12/2 = 6)

Therefore, the ratio that is proportional to 80:60 is 16:12.