f(x)=2x^2+x-4
Find f(-10)

Answer:

x = 10

Step-by-step explanation:

8x + 14 = 6x + 34  (vertically opposite angles are equal)

Rearrange

2x = 20

x = 10

Answer:

x=10

Step-by-step explanation:

So we know that they are equal to each other.

so 6x+34=8x+14

-6x

34=2x+14

-14

20=2x

/2

x=10

The least number of distinct values that can occur in the list is 225.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.

The mode appears 10 times. That leaves 2008 numbers.

The least number of distinct values will occur if all but one of the remaining values appears 9 times

= 2008/9

=223 1/9.

So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.

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The ordered pair in the quadrilateral that represents the coordinates of the corresponding point on A'B'C'D' is B. (0.7x, 0.7y).

An ordered pair consists of two elements arranged in an exact sequence. Mathematics typically denotes this concept by inserting the components into parentheses and splitting them by a comma, (a, b).

Ordered pairs are frequently employed to designate points on a graph or plane where the first member represents the horizontal position (x-coordinate), and the other highlights the vertical dimension (y-coordinate).

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To calculate the amount of soil that needs to be imported or exported in a highway construction project, we need to consider the cut and fill areas, as well as the swell and shrinkage percentages.

In this case, the cut cross sections at Stations 34+00 and 35+00 have areas of 520 and 480 square meters, respectively. The swell percentage is 20% and the shrinkage percentage is 15%.

To calculate the soil volume, we need to multiply the area by the corresponding percentage:

For Station 34+00: Cut area = 520 m², Swell percentage = 20%

Soil volume = Cut area * (1 + Swell percentage/100) = 520 m² * (1 + 20/100) = 520 m² * 1.2 = 624 m³

For Station 35+00: Cut area = 480 m², Swell percentage = 20%

Soil volume = Cut area * (1 + Swell percentage/100) = 480 m² * (1 + 20/100) = 480 m² * 1.2 = 576 m³

Since the swell percentage indicates an increase in soil volume, the soil needs to be imported to the project. The amount of soil to be imported is the difference between the calculated soil volumes and the cut areas:

Soil to be imported = Soil volume - Cut area

For Station 34+00: Soil to be imported = 624 m³ - 520 m² = 104 m³

For Station 35+00: Soil to be imported = 576 m³ - 480 m² = 96 m³

Therefore, a total of 104 cubic meters of soil should be imported at Station 34+00, and 96 cubic meters should be imported at Station 35+00 in the highway construction project.

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Answer:

105

Step-by-step explanation:

Answer:

101 degrees

Step-by-step explanation:

the sum of all angles in a triangle is always 180 degrees.

the other not-shaded angle in the lower triangle is also 42 degrees.

the shaded angle is therefore

180 - 37 - 42 = 101 degrees

median is 16 ducky quack

Answer:

16

Step-by-step explanation:

Median, also known as the "middle" value in a data set. To be able to find the median, your data needs to be in numerical order.

Quiz scores:

9, 13, 20, 15, 18, 17

Arrange in numerical order:

9, 13, 15, 17, 18, 20

Find the "middle" value:

9, 13, 15, 17, 18, 20

When there are two middle values, you add them up and divide it by 2.

15 + 17 = 32

32/2 = 16

Therefore, the median, "middle" value of this student's quizzes is 16.

Hope this helps!

Answer:

Step-by-step explanation:what is the answer for this question

One problem with the arithmetic mean is that it is influenced by outliers. Because with the presence of outliers , the arithmetic mean will be pulled towards the outlier. So, the correct option is A) it is influenced by outliers.

The arithmetic mean is calculated by summing up all the observations in a dataset and dividing by the number of observations. While it is a commonly used measure of central tendency, it has some limitations. One of the main problems with the arithmetic mean is that it can be strongly influenced by outliers.

An outlier is an observation that is very different from the other observations in the dataset. When outliers are present, the arithmetic mean can be pulled towards the outlier and may not be a good representation of the typical value in the dataset.  So, the answer is A) it is influenced by outliers.

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the composite function that can be used to determine the height, in meters, of the flare at any given time is:
h_meters(t) = 0.3048 * h(t)

To determine the height of the flare in meters at any given time, we can use the composite function. The composite function is obtained by converting the height in feet to meters.

The conversion factor to convert feet to meters is 0.3048. So, we can multiply the height in feet by 0.3048 to get the height in meters.

Therefore, the composite function that can be used to determine the height, in meters, of the flare at any given time is:

h_meters(t) = 0.3048 * h(t)  Where h(t) is the height of the flare in feet, and h_meters(t) is the height of the flare in meters.

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The Taylor series formula in summation notation f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n } where f^n(a) denotes the nth derivative of f(t) evaluated at t = a.

Since the functions f(t) and g(t) have not been given in the question, I cannot provide a specific answer to this question. However, I can provide a general approach to finding the power series expansion of a function about a point.

To find the power series expansion of a function f(t) about a point t = a, we can use the Taylor series formula:

f(t) = f(a) + f'(a)(t-a) + (1/2!)f''(a)(t-a)^2 + (1/3!)f'''(a)(t-a)^3 + ...

where f'(a), f''(a), f'''(a), ... are the first, second, third, and higher-order derivatives of f(t) evaluated at t = a.

To find the first four nonzero terms of the power series expansion, we can calculate the values of f(a), f'(a), f''(a), and f'''(a) at t = a, substitute them into the Taylor series formula, and simplify the resulting expression. The first four nonzero terms will be the constant term, the linear term, the quadratic term, and the cubic term.

To find the general term of the power series expansion, we can write the Taylor series formula in summation notation:

f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n }

where f^n(a) denotes the nth derivative of f(t) evaluated at t = a. The general term of the power series expansion is given by the expression in the curly braces. We can use this expression to find any term in the series by plugging in the appropriate values of n and f^n(a).

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Answer:

Full answer: 0.26385224274406332453825857519789 Rounded to the nearest hundredth: 0.26 Rounded to the nearest tenth: 0.3

Step-by-step explanation:

All correct proportions include the following:

A. \(\frac{AC}{CE} =\frac{BD}{DF}\)

D. \(\frac{CE}{DF} =\frac{AE}{BF}\)

In Mathematics and Geometry, two geometric figures are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Hence, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar.

Since line segment AB is parallel to line segment CD and parallel to line segment EF, we can logically deduce that they are congruent because they can undergo rigid motions. Therefore, we have the following proportional side lengths;

\(\frac{AC}{CE} =\frac{BD}{DF}\)

\(\frac{CE}{DF} =\frac{AE}{BF}\)

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The image point for the given rule and preimage is (6 - 8)

When we apply a rule T<a, b> to a preimage point (x, y) we get the image (x + a, y + b), so this is like a translation.

So if we apply the rule T<4, -1> to the preimage point (2, -7), the image will be:

(2 + 4, - 7 + (-1)) = (6 - 8)

Concluding, the image point is (6 - 8)

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Answer:

7=x

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Answer:

the correct answer is -68

The probability is 1, or 100%, that a randomly selected person from this sample believed either the true headline or the false headline.

Probability is a measure of the likelihood or chance that a specific event will occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

The probability that a randomly selected person from this sample believed the true headline or believed the false headline can be calculated by adding the number of people who believed the true headline to the number of people who believed the false headline and dividing by the total sample size.

In this case, the number of people who believed the true headline is 120, and the number of people who believed the false headline is 80. Therefore, the total number of people who believed either headline is 120 + 80 = 200.

The total sample size is also 200, so the probability that a randomly selected person from this sample believed the true headline or believed the false headline is:

(120 + 80) / 200 = 200 / 200 = 1

Therefore, the probability is 1, or 100%, that a randomly selected person from this sample believed either the true headline or the false headline.

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Complete Question:

In a sample of 200 people, 120 believed a true headline and 80 believed a false headline. What is the probability that a randomly selected person from this sample believed the true headline or believed the false headline?

Given:

The graph of system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be \(\leq\).

\(y\leq 10\).

The shaded region lies on the right side of the y-axis. So, \(x\geq 0\).

Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-1=\dfrac{2-1}{1-0}(x-0)\)

\(y=1(x)+1\)

\(y=x+1\)

The boundary line \(y=x+1\) is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be \(>\).

\(y> x+1\)

So, the required system of inequalities is:

\(y> x+1\)

\(y\leq 10\)

\(x\geq 0\)

Therefore, the correct option is B.

Hey!! Glad I can help!!!

Answer:

-16.25+20=3.75

Step-by-step explanation:

the negative sign is outside the box so it does not affect the absolute value.

then do -16.25+20 and you get 3.75.

If satisfied leave a review and feel free to give brainiest.

Answer: 1. You have to solve -|16.25| first, which the answer is -16.25. 2. Now you add 20. -16.25+20=3.75

Step-by-step explanation:

Answer:

The products of -3(1) and -3(-1) are the same because both expressions result in the multiplication of -3 and a number, where one of the numbers is positive and the other is negative. The product of these two numbers is always negative.

Step-by-step explanation:

-3(1) means multiplying -3 by 1, which gives -3 as the product.

-3(-1) means multiplying -3 by -1, which gives 3 as the product.

Even though the two expressions are different, we can see that both involve multiplying -3 with a number, where one of the numbers is positive and the other is negative.

When we multiply a negative number and a positive number, the product is always negative. Similarly, when we multiply a negative number and a negative number, the product is always positive.

So, in both -3(1) and -3(-1), we are multiplying a negative number (-3) with a positive number (1 in the first expression and -1 in the second expression). Therefore, the products of both expressions are negative (-3 in the first expression and 3 with a negative sign in the second expression).

Hence, we can conclude that the products of -3(1) and -3(-1) are the same and equal to -3.

Answer:

It should be -5

Step-by-step explanation:

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

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Thus,  to determine the minimum dbar diameter to prevent fatigue failure, you need to consider the load cycles, material properties, stress range, structural design, and safety factor.

To determine the minimum reinforcing bar (dbar) diameter to ensure that fatigue failure will not occur, you need to consider the following factors:

1. Load Cycles: Fatigue failure typically occurs when a material is subjected to repeated cycles of stress. Analyze the expected number of load cycles and their magnitudes during the structure's service life.

2. Material Properties: The fatigue strength of the reinforcing bars depends on their material properties, such as yield strength, tensile strength, and ductility. Choose a dbar material that can withstand the anticipated stress cycles without causing fatigue failure.

3. Stress Range: Calculate the stress range (the difference between the maximum and minimum stress) the dbar will experience during the load cycles. This will help you assess the fatigue resistance of the material.

4. Structural Design: Optimize the structural design to minimize stress concentration and ensure uniform distribution of loads. This can help reduce the risk of fatigue failure.

5. Safety Factor: Apply an appropriate safety factor to account for uncertainties in material properties, load cycles, and structural design. This factor will help you determine a conservative minimum dbar diameter that reduces the risk of fatigue failure.

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Based on the description, it is not possible to provide a specific answer without a visual representation of the dot plot. However, I can explain each term and help you identify the correct answer once you examine the dot plot.


a) Approximately normal: The dot plot would resemble a bell curve, with most points centered around the mean and symmetrically distributed on both sides.
b) Bimodal without a gap: The dot plot would have two distinct peaks, but the points are continuous and do not have a gap between them.
c) Bimodal with a gap: The dot plot would have two distinct peaks, with a clear gap separating them.
d) Skewed to the right without a gap: The dot plot would have a longer tail on the right side, indicating higher values, with no gap in the data.
e) Skewed to the right with a gap: The dot plot would have a longer tail on the right side, indicating higher values, and a clear gap in the data.

To determine the correct answer, examine the dot plot and identify its shape based on the explanations provided above. Then, choose the option that best describes the dot plot.

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The equation of the sphere is: x² - 11x + (5/2)y - z² + 6z + 5/6 = 0

Let the center of the sphere be denoted by (h, k, l) and the radius be denoted by r. The sphere's equation can thus be expressed as follows:

(x - h)² + (y - k)² + (z - l)² = r²

We are given that the distance from P to A is twice the distance from P to B. Let d(P, A) and d(P, B) be the distances from P to A and B, respectively. Then we have:

d(P, A) = 2*d(P, B)

Using the distance formula, we can express d(P, A) and d(P, B) as follows:

d(P, A) = sqrt((x + 2)² + (y - 4)²+ (z - 4)²)

d(P, B) = sqrt((x - 5)² + (y - 2)² + (z + 2)²)

When we simplify the equation above and substitute these, we obtain:

(x - h)² + (y - k)² + (z - l)² = 5(x - h - 7)² + (y - k - 2)² + (z - l + 6)²

Expanding and collecting like terms, we obtain:

4x² - 44x - 8y + 92 + 4z² - 24z - 3h² - 3k² - 3l² + 90h + 40k - 72l + 285 = 0

This is the sphere's standard form equation. Comparing coefficients with the standard form, we can identify the center and radius as follows:

Center: (h, k, l) = (11/3, -5/3, -5)

Radius: r = sqrt(3/4*((11/3)^2 + (-5/3)² + (-5)² - 285))

Therefore, the equation of the sphere is:

4x² - 44x - 8y + 92 + 4z² - 24z - 3(11/3)² - 3(-5/3)² - 3(-5)² + 90(11/3) + 40(-5/3) - 72(-5) + 285 = 0

Simplifying, we get:

4x² - 44x - 8y + 4z² - 24z - 10/3 = 0

or, equivalently:

x² - 11x + (5/2)y - z² + 6z + 5/6 = 0

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Answer:

I think it's 79

Step-by-step explanation:

.... Hi don't be mad if you get wrong

Answer:

80 - 16 ÷ 8   80 - 2= 78

Step-by-step explanation:

The polar equation r = 2 sin θ is equivalent to the rectangular equation y = x tan θ.

The polar equation is r=2sinθ. To convert it into rectangular form, we can use the identities x = r cos θ and y = r sin θ.

Replacing r with 2 sin θ, we get x = 2 cos θ sin θ and y = 2 sin^2 θ. Simplifying these expressions using the identity sin^2 θ + cos^2 θ = 1, we get the rectangular equation y = x sin θ / cos θ, which can also be written as y = x tan θ.

Thus, the polar equation r = 2 sin θ is equivalent to the rectangular equation y = x tan θ.

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Answer: 5.46 billion

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

Explanation:

If you mean the world's population, then there are roughly 7.8 billion people on earth.

70% of that is 0.70*7.8 = 5.46 billion

The number 5.46 billion can be written as 5,460,000,000

This number is read out as "5 billion, 460 million"

Ans .: The dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

To minimize the cost of the container, we need to find the dimensions that will use the least amount of material. Let's call the length of one side of the square base "x" and the height of the container "h".

The volume of the container is given as 2000 cm^3, so we can write:

V = x^2h = 2000

We need to find the dimensions that will minimize the cost, which is determined by the amount of material used. We know that it costs twice as much per square centimeter to make the top and bottom as it does the sides.

Let's call the cost per square centimeter of the sides "c", so the cost per square centimeter of the top and bottom is "2c". The total cost of the container can then be expressed as:

Cost = 2c(x^2) + 4(2c)(xh)

The first term represents the cost of the top and bottom, which is twice as much as the cost of the sides. The second term represents the cost of the four sides.

To minimize the cost, we can take the derivative of the cost function with respect to "x" and set it equal to zero:

dCost/dx = 4cx + 8ch = 0

Solving for "h", we get:

h = -0.5x

Substituting this into the volume equation, we get:

x^2(-0.5x) = 2000

Simplifying, we get:

x^3 = -4000

Taking the cube root of both sides, we get:

x = -16.7

Since we can't have a negative length, we take the absolute value of x and get:

x = 16.7 cm

Substituting this into the equation for "h", we get:

h = -0.5(16.7) = -8.35

Again, we can't have a negative height, so we take the absolute value of "h" and get:

h = 8.35 cm

Therefore, the dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

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