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f(x) = 3x2 + 4x − 9,  the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This can be written in interval notation as [−9, ∞).

Interval notation is a mathematical notation used to express the range of a variable. It is used to represent intervals on the number line, either on the real line or on the complex plane.

In this case, the domain of f(x) = 3x2 + 4x − 9 is all real numbers. The range of this function is all real numbers greater than or equal to -9. This can be written in interval notation as [−9, ∞).

The function is a quadratic polynomial of the form ax2 + bx + c. The domain of a polynomial function is all real numbers (i.e. any x-value). The range of the function is the set of all y-values that it can produce.

Here the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This means that the minimum y-value that the function can produce is -9. This means that the range of the function is all real numbers greater than or equal to -9.

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The relationship between the mean and median depends on the shape of the distribution of the data, therefore correct options are

(a) The mean is approximately the same as the median

(b) The mean is greater than the median

(c)  The mean is less than the median.

The relationship between the mean and the median depends on the shape of the distribution of the data. In a symmetric distribution, the mean and median will be approximately the same. In a skewed distribution, the mean will be pulled in the direction of the skew, and the median will be a better representation of the "typical" value.

If the distribution is symmetrical (i.e., evenly distributed around the center), the mean and median will be approximately the same.

If the distribution is positively skewed (i.e., has a long tail on the right side), the mean will be greater than the median.

If the distribution is negatively skewed (i.e., has a long tail on the left side), the mean will be less than the median.

Therefore, correct options are

(a) The mean is approximately the same as the median

(b) The mean is greater than the median

(c)  The mean is less than the median.

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If a water bottle contains 375 ml, So the volume in quarts is 0.396 qt.

       The volume of a water bottle containing 375 ml can be converted into a quart using the conversion formula.

          One can use the following conversion formula to convert a given volume in ml to quarts.

          The conversion formula for ml to quarts is given as;

                      1 ml = 0.00105669 quarts

Volume in quarts = Volume in ml × 0.00105669

     Now, to calculate the volume of 375 ml of the water bottle in quarts,

     We will substitute the given volume in the above conversion formula as follows,

      Volume in quarts = 375 ml × 0.00105669

                                    = 0.396 qt

       Hence, the volume of the water bottle containing 375 ml is 0.396 qt.

      Therefore, the correct option is C. 0.396 qt.

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Answer: True.

Step-by-step explanation:

Important differences are always statistically significant if small sample size is used

1.  Exponential decay 2. Josh's function represents the situation correctly 3. V(x) = 1275(0.835)ˣ,  V(x) = 1275(1-0.165)ˣ

An exponential decay function is a mathematical function that describes the decrease in value of a quantity over time or through a series of events. It is often used to model natural phenomena such as radioactive decay or the spread of diseases.

In an exponential decay function, the value of the quantity decreases exponentially over time. This means that the rate of decrease is proportional to the value of the quantity at any given time.

The exponential decay function is characterized by a decreasing graph that approaches zero but never touches the x-axis. The rate of decay slows down over time, but the quantity never completely disappears. The function is used in various fields such as physics, chemistry, biology, finance, and economics, to name a few.

1. This situation represents exponential decay because the value of the computer decreases by 16.5% each year.

2. Josh's function represents the situation correctly because it involves the decay factor (0.835) which is less than 1, reflecting the decrease in value each year. Eve's function represents exponential growth which is not consistent with the situation where the value of the computer decreases each year.

3. V(x) = 1275(0.835)ˣ represents the function using the form V(x) = a(b)ˣ where a = 1275 and b = 0.835.

Alternatively, V(x) = 1275(1-0.165)ˣ represents the function using the form V(x) = a(1-r)ˣ where a = 1275 and r = 0.165.

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We can say with 95% confidence interval that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

To calculate the confidence interval, we use the formula:

CI = x-bar ± z* (σ/√n)

where x-bar is the sample mean (50,000 miles), z is the z-score associated with the desired confidence level (in this case, 1.96 for 95% confidence level), σ is the standard deviation (5,000 miles), and n is the sample size (100).

Plugging in the values, we get:

CI = 50,000 ± 1.96*(5,000/√100)

Simplifying the expression, we get:

CI = 50,000 ± 980.

Therefore, we can say with 95% confidence that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

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P(a number greater than 5 and an even number) = 1/6 or 0.167

Part 1 of 3 (a) To find the probability of getting an even number, divide the number of favorable outcomes (rolling a 2, 4, or 6) by the total possible outcomes (rolling any number between 1 and 6). There are 3 even numbers and 6 total possible outcomes.

P(an even number) = [tex]3/6 = 1/2 or 0.500[/tex]

Part 2 of 3 (b) To find the probability of getting a number less than or equal to 4, count the favorable outcomes (rolling a 1, 2, 3, or 4) and divide by the total possible outcomes (6). There are 4 favorable outcomes and 6 total possible outcomes.

P(a number less than or equal to 4) =[tex] 4/6 = 2/3 or 0.667[/tex]

Part 3 of 3 (c) To find the probability of getting a number greater than 5 and an even number, count the favorable outcomes (rolling a 6) and divide by the total possible outcomes (6). There is 1 favorable outcome and 6 total possible outcomes.

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Hence, the best descriptors for each scatterplot are identified in the answer.

Scatterplots: Identifying the best descriptors for each scatterplot Here are the scatterplots (a) and (b). a) Scatterplot (a) From the above scatterplot, the best descriptors are: Weak Relationship (There is no strong correlation between the two variables)Linear Relationship (The data points follow a linear pattern)Approximate Relationship (The data points appear to follow an approximate trend)No Relationship (There is no correlation between the two variables) b) Scatterplot (b) From the above scatterplot, the best descriptors are :No Relationship (There is no correlation between the two variables)Moderate Relationship (There is a moderate correlation between the two variables)Deterministic Relationship (The relationship between the variables is deterministic and direct)Strong Relationship (There is a strong correlation between the two variables)

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In cubic equation the point P is (-3, 0) and the ratio AP/PB is (-3 - (-1))/(10 - (-3)) = 2/3.

What is cubic equation ?

A cubic equation is a polynomial equation of the third degree, meaning it contains a variable with an exponent of 3, and it is of the form ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants and a is not equal to 0. The solutions to a cubic equation can be found using various methods, such as factoring, the rational root theorem, and the cubic formula.

According to the question:
We know that point P lies on the x-axis. Therefore, the y-coordinate of point P is 0.

Let the x-coordinate of point P be k.

Since point P divides the line segment AB in the ratio k : 1, we have:

AP/PB = k/1

Using the distance formula, we can find the lengths of AP and PB:

[tex]AP = sqrt[(k - (-1))^2 + (0 - (-2))^2] = sqrt[(k + 1)^2 + 4][/tex]

[tex]PB = sqrt[(k - (-10))^2 + (0 - 7)^2] = sqrt[(k + 10)^2 + 49][/tex]

Therefore, we have:

[tex]sqrt[(k + 1)^2 + 4]/sqrt[(k + 10)^2 + 49] = k/1[/tex]

Squaring both sides, we get:

[tex][(k + 1)^2 + 4]/[(k + 10)^2 + 49] = k^2[/tex]

Expanding the numerator and denominator, we get:

[tex]k^4 + 18k^3 + 133k^2 + 410k + 405 = 0[/tex]

Using synthetic division or a calculator, we can find that this equation factors as:

[tex](k + 5)(k^3 + 13k^2 + 58k + 81) = 0[/tex]

The factor k + 5 corresponds to the case where P is the midpoint of AB, which does not lie on the x-axis.

Therefore, we must solve the cubic equation [tex]k^3 + 13k^2 + 58k + 81 = 0[/tex] to find the value of k that satisfies the given conditions.

Using synthetic division or a calculator, we find that the cubic equation factors as:

[tex](k + 3)(k^2 + 10k + 27) = 0[/tex]

Therefore, the solutions are k = -3 and k = -5.

Since P lies on the x-axis, we choose the solution k = -3.

Therefore, the point P is (-3, 0) and the ratio AP/PB is (-3 - (-1))/(10 - (-3)) = 2/3.

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(a) To find P(0 < Z < 2.74), you'll want to look up the z-score for 2.74 in a standard normal table or use a calculator with a built-in normal distribution function. The probability is the area under the curve between 0 and 2.74.

(b) To find P(0 < Z < 1), you'll look up the z-score for 1 in a standard normal table or use a calculator. The probability is the area under the curve between 0 and 1.

(c) To find P(-2.40 < Z < 0), you'll look up the z-score for -2.40 in a standard normal table or use a calculator. The probability is the area under the curve between -2.40 and 0.

(d) To find P(-2.40 < Z < 2.40), you can first calculate the probability for P(-2.40 < Z < 0) and P(0 < Z < 2.40), and then sum the two probabilities.

(e) To find P(Z > 1.63), look up the z-score for 1.63 in a standard normal table or use a calculator. The probability is the area under the curve to the right of 1.63.

(f) To find P(Z < -1.74), look up the z-score for -1.74 in a standard normal table or use a calculator. The probability is the area under the curve to the left of -1.74.

(g) To find P(-1.4 < Z < 2.00), first look up the z-scores for -1.4 and 2.00 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

(h) To find P(1.63 < Z < 2.50), first look up the z-scores for 1.63 and 2.50 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

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The first thing the surveyor did when he surveyed the new neighborhood was to reference the legal description of the property.

A legal description is a precise way of identifying and describing real estate in a manner that is legally sufficient to enable it to be transferred, sold, or mortgaged. Legal descriptions can take various forms, including metes and bounds, government rectangular survey, and lot and block descriptions.

In the case of Happy Acres, the surveyor created a lot and block survey for the new residential development. In this type of survey, the lots are identified by a number or letter, and the blocks are identified by a number.

This type of description is based on a recorded plat, which is a map or plan of a subdivision that has been legally recorded with the appropriate government agency.

Before creating the lot and block survey, the surveyor would have first referenced the legal description of the property, which would have provided the necessary information to accurately locate and describe the boundaries of the new development.

This legal description could have been obtained from various sources, including deeds, recorded plats, and other legal documents.

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The plane's average speed in still air is 270 mph.

The plane's average speed in still air can be calculated as follows:

x = Speed of plane in still air (unknown)            y = Speed of wind (unknown)

Speed of plane with wind = (x + y)

Speed of plane against wind = (x - y)

Using the formula, distance = speed x time, we can equate the above quantities to get two equations as shown below:

1200 = 4(x + y) ... (i)

1200 = 5(x - y) ... (ii)

Simplifying equation (i) and (ii), we get:

x = 270

Therefore, the plane's average speed in still air is 270 mph.

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The best type of inspection to use depends on the nature of the purchase. Each type of inspection has its own advantages and disadvantages, and should be chosen based on the requirements of the product and the level of risk associated with the inspection.

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Answer:  4

Step-by-step explanation:

Given when y = 2,   x =  -2

Therefore  2 = -2 + ?

? = 2 + 2

? = 4

Answer:

Step-by-step explanation:

We are given the equation:

y = 0.125x² - 569x + 848000

And we are asked to find the range of values of x for which y is less than $400,000 per million board feet.

Substituting $400,000 for y, we get:

$400,000 = 0.125x² - 569x + 848000

Simplifying this equation, we get:

0.125x² - 569x + 448000 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b² - 4ac))/(2a)

where a = 0.125, b = -569, and c = 448000.

Plugging in these values, we get:

x = (-(-569) ± sqrt((-569)² - 4(0.125)(448000)))/(2(0.125))

x = (569 ± sqrt(322961))/0.25

x = (569 ± 569.39)/0.25

x ≈ 1163.57 or x ≈ 68.43

However, we need to check if these values satisfy the given condition of 400 5 x ≤ 2200.

Only x ≈ 68.43 satisfies this condition. Therefore, the harvested timber volume for which the value of the timber is less than $400,000 per million board feet is approximately 68.43 million board feet.

The location of the other 2 fountains, given the coordinates of the fountain would be (-6, 6) and (0, 6).

The fountain at (-3, 6) is located exactly in the middle of the horizontal line segment between the other two fountains, so the distance between each of the other two fountains and the middle fountain is 3 units (half of the total distance of 6 units).

Since the line segment is horizontal, the y-coordinate for both fountains will be the same as the middle fountain, which is 6.

Now we need to find the x-coordinates. We'll add 3 units to the x-coordinate of the middle fountain for one of the other fountains and subtract 3 units for the other one:

Fountain A: (-3 - 3, 6) = (-6, 6)

Fountain B: (-3 + 3, 6) = (0, 6)

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True, the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.

what is a triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles. It is one of the most basic and fundamental shapes in geometry.

The image shows a transformation where the figure has been moved to a different position while maintaining its size and shape. This type of transformation is called a translation, which involves sliding an object in a particular direction without changing its size or shape.

To perform a translation, we need to know how far the object has been moved horizontally and vertically. In the image, we can see that the blue triangle has been moved 2 units to the right and 3 units up. We can represent this translation using vector notation, where the vector (2, 3) represents the horizontal and vertical distances that the triangle has been moved.

Therefore, true the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.

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The percentage of scores greater than 34 is 0.5398 or 53.98%.

Given that the mean of scores (μ) = 35 and the standard deviation (σ) = 10. We need to find the percentage of scores greater than 34. Since the scores are normally distributed, we can standardize the variable by using the z-score formula.

z = (x - μ) / σ

Here, x = 34, μ = 35 and σ = 10z = (34 - 35) / 10z = -0.1

We need to find the area to the right of the z-score line on the standard normal distribution table. The standard normal distribution table provides the probabilities corresponding to the z-scores, i.e. the area under the curve to the right or left of the z-score line on the distribution table. The area to the right of the z-score line represents the percentage of scores that are greater than the given value. Using the standard normal distribution table, the area to the right of the z-score line -0.1 is 0.5398.

The percentage of scores greater than 34 is 0.5398 or 53.98%.

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The vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.

A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function. The equation of a parabola in standard form is y = ax² + bx + c, where "a", "b", and "c" are constants, and "x" and "y" are variables.

a. To evaluate h(0), we substitute t=0 in the equation:

h(0) = 15 + 7(0) - 16(0)² = 15

This means that at the instant the boy throws the rock (t=0), the height of the rock is 15 feet above the ground.

b. To estimate the time when the rock hits the ground, we need to find the value of t when h(t) = 0. We can solve the equation 15 + 7t - 16t² = 0 for t, using the quadratic formula:

t = (-7 ± √(7² - 4(-16)(15))) / (2(-16))

t ≈ 1.28 s or t ≈ 1.97 s

This means that the rock will hit the ground approximately 1.28 seconds or 1.97 seconds after it is thrown.

c. The equation h(1) = 6 means that one second after the rock is thrown, its height above the ground is 6 feet.

d. The vertex of the parabola h(t) = 15 + 7t - 16t² can be found by using the formula t = -b/2a, where a=-16 and b=7.

t = -7 / (2(-16)) = 7/32

Substituting t=7/32 into the equation, we get:

h(7/32) = 15 + 7(7/32) - 16(7/32)² ≈ 17.2

Therefore, the vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.

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a. (x + 6)(x + 6) expands and simplifies to x² + 12x + 36.

b. (x + 8)(x - 5) expands and simplifies to x² + 3x - 40.

c. (x - 5)(x - 2) expands and simplifies to x² - 7x + 10.

Expansion and simplification are two related processes in algebra that involve manipulating mathematical expressions. Expansion involves multiplying out the terms in an expression to get a longer form, while simplification involves reducing an expression to a shorter, more manageable form.

In the given question,

a.To expand and simplify (x + 6)(x + 6), we can use the distributive property as follows:

(x + 6)(x + 6) = x(x + 6) + 6(x + 6)= x² + 6x + 6x + 36= x² + 12x + 36.

b.To expand and simplify (x + 8)(x - 5), we can use the distributive property as follows:

(x + 8)(x - 5) = x(x - 5) + 8(x - 5)= x² - 5x + 8x - 40= x²+ 3x - 40

Therefore, (x + 8)(x - 5) expands and simplifies to x²+ 3x - 40.

c.To expand and simplify (x - 5)(x - 2), we can use the distributive property as follows:

(x - 5)(x - 2) = x(x - 2) - 5(x - 2)= x² - 2x - 5x + 10= x²- 7x + 10

Therefore, (x - 5)(x - 2) expands and simplifies to x² - 7x + 10.

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Answer:

Step-by-step explanation:

-8+35 = 27

-16+4 = -12 but when you take the absolute value it turns positive.

So 27+ 12 is 39

The probability that a patient would have a depression score greater than 60 is 0.9878.

The probability that a patient would have a depression score greater than 60 in a pain clinic when the mean depression score on a sample of patients is 78 with a standard deviation of 8 can be calculated using z-score.

Z-score formula

Z-score = (x - μ) / σ

Where,

x = the value to be standardized

μ = the mean of the population

σ = the standard deviation of the population

Given data,

Mean = 78

Standard deviation, σ = 8

Let x be the depression score.

To find the probability that a patient would have a depression score greater than 60, we need to find the z-score first.

Using the formula,

z-score = (x - μ) / σ = (60 - 78) / 8 = -2.25

Now, the probability can be calculated using the z-score table which gives the probability that a value will be less than z.

To find the probability that a value will be greater than z, subtract the probability from 1.

Probability of Z < -2.25 = 0.0122

Probability of Z > -2.25 = 1 - 0.0122 = 0.9878

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Alice gave Zack 3/32 of the full bar of chocolate, which is equal to 1/4 of Alice's own piece.

Alice got 5/8 of a full bar of chocolate, which means she consumed 3/8 of the full bar. Now, Zack got 1/4 of the full bar from Alice, which means Alice gave him 1/4 of her own piece.

To calculate the amount of chocolate that Alice gave to Zack, we need to find out how much 1/4 of Alice's piece is. Since Alice consumed 3/8 of the full bar, her piece is equal to 3/8 of the full bar. Therefore, to find 1/4 of Alice's piece, we need to multiply 3/8 by 1/4:

3/8 * 1/4 = 3/32

So Alice gave Zack 3/32 of the full bar of chocolate.

To put it another way, Alice gave away 1/8 of the full bar of chocolate (since 5/8 - 3/8 = 1/8), and Zack received 1/4 of that 1/8, which is equal to 1/32 of the full bar. Therefore, Alice gave Zack 3/32 of the full bar of chocolate.

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The statement "A global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors." is the correct .

Therefore option C is correct.

What is a global firm?

A global firm is a company that operates in more than one country and has access to research and development, production, logistical, marketing, and financial advantages that are not available to purely domestic rivals.

Global companies have expanded beyond their home country's boundaries to capitalize on the advantages of global sourcing and production.

Global companies have a variety of advantages that pure domestic companies do not have.

The following are some of the benefits of global businesses:

In conclusion, a global firm is a firm that operates in more than one country and captures R&D, production, logistical, marketing, and financial advantages not available to purely domestic competitors.

Therefore option C is correct.

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The price in dollars per square yard is approximately $23.04.

To convert from pounds per square meter to dollars per square yard, we need to use the conversion rates between currencies and units of area.

First, we convert pounds to dollars using the current exchange rate. The exchange rate is approximately 1.38 dollars per pound, so 16 pounds per square meter is equivalent to approximately 22.08 dollars per square meter.

Next, we convert square meters to square yards. There are 1.196 square yards in a square meter, so the price in dollars per square yard is approximately:

22.08 dollars per square meter ÷ 1.196 square yards per square meter ≈ 18.43 dollars per square yard.

Therefore, the price in dollars per square yard is approximately $23.04, rounded to two decimal places.

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answer

6 divided by 54 is equal to 9

therefore

answer = d=9

Answer:

m = 50 + 6

m= 56

lol easy ques

This one is easy. All you have to do is add 6 to both sides to get the value of m

m-6=50

m=50+6

m=56

(This graph is difficult to read because of the poor photo quality)

For lateral and vertical translations drag each point one unit to the left and two units down.

The upper left point will go to (0,-4)

The upper right point will go to (8,-4)

The bottom left point will go to (0,-9)

The middle point will go to (3,-7)

The last point will go to (6,-8)

The translated shape will be the same as the new shape!

Answer:

Hi

Step-by-step explanation: