1) Name the independent variable. Y= 12x + 25 *
10 points

A discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.

The main difference between a discrete function and a continuous function lies in the nature of their domains and ranges. A discrete function is defined on a set of distinct, separate values, while a continuous function is defined on a continuous interval or range of values.

A discrete function can be thought of as a function that consists of isolated points. For example, let's consider a function that represents the number of students in a classroom over the years. The domain of this function would be the set of discrete values representing each year, such as {2010, 2011, 2012, ...}. The range would be the set of corresponding numbers representing the number of students in the classroom each year.

On the other hand, a continuous function is one that can take on any value within a given interval. For instance, consider a function that represents the temperature in a room over time. The domain of this function would be a continuous interval, such as [0, 24] representing the 24-hour day. The range would be the set of possible temperature values within that interval.

To summarize, a discrete function is defined on distinct values, while a continuous function is defined on a continuous interval. Discrete functions consist of isolated points, while continuous functions can take on any value within a given range.
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Answer:

Step-by-step explanation:

A) Two similar solids have a scale factor of 3:5. If the height of solid I is 3 cm, find the height of solid II (B) If the surface area of 1 is 54π cm, fine

Answer:

D

Step-by-step explanation:

The sin is equal to the opposite of the chord

The equation of the line l that passes through the points (0, -4) and (2, 0) is y = 2x - 4.

The correct option is B.

As per the diagram, the equation of the line l passes through two points (0, -4) and (2, 0).

To find the equation of the line l that passes through the points (0, -4) and (2, 0), we need to first find the slope of the line.

The slope of the line is given by:

m =  (y₂- y₁) / (x₂ - x₁)

where (x1, y1) = (0, -4) and (x2, y2) = (2, 0).

m = (0 - (-4)) / (2 - 0) = 4 / 2 = 2

Therefore, the steepness of the line is 2.

Now, we can use the point-slope form of the equation of a line to write the equation of the line l.

The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) is the representation of one of the points on the line, and m is described as the slope of the line.

Let's use the point (0, -4) as our reference point:

y - (-4) = 2(x - 0)

Simplifying this equation, we get:

y + 4 = 2x

Subtracting 4 from both sides, we get the final equation of the line:

y = 2x - 4

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The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.

For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.

The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.

Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.

Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.

This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.

Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.

The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.

Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.

Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the  answer is (b) S = 2231.

The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

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\(5 + n = 12 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

Answer:

The correct answer is m=3w+y/-3

Answer:

Is it C. 20/29

Step-by-step explanation:

because 20 and 29 are right next to it.

Based on the information provided, the suggested interval (0 < x < 2) could potentially be an interval during which the water balloon's height is increasing.

In general, if the height of the water balloon is increasing, it means that as time progresses, the height of the balloon is getting larger. This corresponds to a positive rate of change of the height with respect to time.

If we have a function that describes the height of the water balloon over time, we can calculate the derivative of that function with respect to time. If the derivative is positive within the interval (0 < x < 2), it means that the height is increasing during that interval.

However, without the specific function or more information, it is not possible to determine with certainty whether the water balloon's height is increasing within the given interval.

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The required coordinate of point P is (-5, 4)

We can use the concept of section formula to find the coordinates of the point P that partitions the segment MN in the ratio of 4 to 6.

Let the coordinates of point P be (x, y). Then, using the section formula, we have:

x = (6*(-5) + 4*(-5))/10 = -5 [using the x-coordinate of M and N, and the ratio of 4:6]

y = (68 + 4(-2))/10 = 4 [using the y-coordinate of M and N, and the ratio of 4:6]

Therefore, the coordinates of point P are (-5, 4).

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Answer:

look at the picture i have sent

The relationship between the determinant of a square matrix and the determinant of the matrix multiplied by a scalar is,  the determinant of the matrix multiplied by a scalar is \(k^{n}\) times the determinant of a square matrix, det(kA) = \(k^{n} D\)

Let A be a square matrix,

And the det(A) = D, equation (1)

If we multiply the square matrix with a scalar k, then the matrix becomes, kA, and its determinant is given as,

det(kA) = \(k^{n} D\) , equation (2)

where k is the scalar,

n is the order of the square matrix and

Dis the determinant of the square matrix A.

Thus, the relationship between the determinant of a square matrix and the determinant of the matrix multiplied by a scalar is,  the determinant of the matrix multiplied by a scalar is \(k^{n}\) times the determinant of a square matrix.

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the p-value (0.208) is greater than the significance level (0.01), we fail to reject the null hypothesis

To determine if there is evidence to suggest that the proportion of voters who believe pharmaceutical companies invent diseases to make money is different for Democrats and Republicans, we can perform a hypothesis test. Let p1 be the proportion of Democrats who believe in the conspiracy theory, and p2 be the proportion of Republicans who believe in the conspiracy theory.

Let's set up the hypotheses:

Null hypothesis (H0): p1 - p2 = 0 (There is no difference in the proportions of Democrats and Republicans who believe in the conspiracy theory)

Alternative hypothesis (Ha): p1 - p2 ≠ 0 (There is a difference in the proportions of Democrats and Republicans who believe in the conspiracy theory)

We will use a two-sample proportion test to test these hypotheses. The test statistic for this test is given by:

\(\[ Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}} \]\)

where:

- \(\( \hat{p}_1 \)\) and \(\( \hat{p}_2 \)\) are the sample proportions of Democrats and Republicans who believe in the conspiracy theory, respectively.

- n₁ and n₂ are the sample sizes of Democrats and Republicans, respectively.

- \(\( \hat{p} \)\) is the overall proportion of belief in the conspiracy theory, calculated as the total number of believers divided by the total sample size.

The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true.

Given the sample data:

Democrats: n₁ = 788 and \(\( \hat{p}_1 = \frac{137}{788} \)\)

Republicans: n₂ = 866 and \(\( \hat{p}_2 = \frac{105}{866} \)\)

Let's calculate the test statistic and the p-value:

Step 1: Calculate \(\( \hat{p} \)\):

Total number of believers = 137 + 105 = 242

Total sample size = 788 + 866 = 1654

\(\( \hat{p} = \frac{242}{1654} \)\)

Step 2: Calculate the test statistic (Z):

\(\[ Z = \frac{\frac{137}{788} - \frac{105}{866}}{\sqrt{\frac{242}{1654} \cdot \left(1 - \frac{242}{1654}\right) \cdot \left(\frac{1}{788} + \frac{1}{866}\right)}} \]\)

≈ -1.258

Step 3: Calculate the p-value using the standard normal distribution table for a two-tailed test.

To calculate the p-value, we need to find the probability that a standard normal distribution is less than or greater than the absolute value of the test statistic. Since the alternative hypothesis is two-sided (p1 ≠ p2), we will calculate the p-value as twice the probability of the test statistic being greater than the absolute value of the calculated z-value.

Using a standard normal distribution table or a statistical software, we find that the p-value is approximately 0.208.

Conclusion:

Since the p-value (0.208) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is insufficient evidence to suggest that the proportion of voters who believe pharmaceutical companies invent diseases to make money is different for Democrats and Republicans.

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Answer:

a rational number

Step-by-step explanation:

a rational number + a rational number will always be a rational number.

Answer:

x=-2

Step-by-step explanation:

2x+7=-9-6x

add 6x on both sides

8x+7=-9

subtract 7 on both sides

8x=-16

x=-2

Answer:

x=-2

Step-by-step explanation:

Let me know if I need to explain but here is the answer cause i know you are in a rush.

Answer:

-13

Step-by-step explanation:

Answer:

t = -13

Step-by-step explanation:

2.6 = -0.2t         Equation

2.6 / -0.2 . = -0.2t/-0.2          Divide -0.2 on both sides

t = - 13       Simplify

Answer:

A) 12

You know:

AB= 3x

AB= 3xAC= 17

AB= 3xAC= 17BC= 2x-3

Therefore, you can put the values in a number line for reference. By doing this you can see that 3x + 2x -3 (or AB +BC) = 17 (or AC)

From here you can set up the equation to be:

17 = 2x - 3 + 3x

and solve for x by combining like terms:

17= 5x-3

adding 3 to both sides:

20=5x

dividing each side by 5:

20/5=5x/5

to get:

x=4

then, you're gonna plug in your x (4) into 3x (your AB) in order to solve for AB:

AB=3x

AB=3x =3(4)

AB=3x =3(4) =12

therefore, your answer is:

AB = 12

Answer:

508.94 in²

Step-by-step explanation:

The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

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We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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Answer:

B = 40° and D = 60°

Step-by-step explanation:

Just subtract the angles you already know from 90° (since perpendicular means right angle, which is 90°).

Answer:

correct

Step-by-step explanation:

The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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To find the work done in pumping the entire contents of the fuel tank into the tractor, we need to calculate the potential energy difference between the initial position of the gasoline in the truck's tank and its final position in the tractor's tank.

Given:

- Diameter of the cylindrical gasoline tank: 4 feet

- Length of the cylindrical gasoline tank: 5 feet

- Opening on the tractor tank is 5 feet above the top of the tank in the truck

First, let's calculate the volume of the cylindrical gasoline tank using the formula for the volume of a cylinder:

Volume = π * (radius^2) * height

The radius of the tank is half the diameter, so the radius is 4 feet / 2 = 2 feet.

Volume = π * (2^2) * 5 = 20π cubic feet

Since the entire contents of the fuel tank need to be pumped, the volume of gasoline to be pumped is 20π cubic feet.

To calculate the work done in pumping the gasoline, we need to find the vertical height through which the gasoline is lifted. This height is the sum of the height of the tank and the distance between the top of the tank and the opening on the tractor tank.

Height = 5 feet + 5 feet = 10 feet

The work done in pumping the gasoline can be calculated using the formula:

Work = Force × Distance

In this case, the force is the weight of the gasoline, and the distance is the height through which it is lifted. To calculate the weight of the gasoline, we need to know the density of gasoline. The density of gasoline can vary, but an average value is around 6.3 pounds per gallon.

Let's convert the volume of gasoline from cubic feet to gallons:

1 cubic foot = 7.48052 gallons (approximately)

Volume in gallons = 20π * 7.48052 ≈ 149.61π gallons

Weight of gasoline = Volume in gallons * Density of gasoline

Assuming the density of gasoline as 6.3 pounds per gallon:

Weight of gasoline = 149.61π * 6.3 ≈ 940.06π pounds

Finally, we can calculate the work done:

Work = Weight of gasoline * Height

Work = 940.06π * 10 ≈ 9400.6π foot-pounds

Therefore, the work done in pumping the entire contents of the fuel tank into the tractor is approximately 9400.6π foot-pounds.

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The company should use a warranty period that is equal to 67,467.5 miles.

To determine the warranty period, we need to find the value of the tire life that corresponds to 95% of the tires. We can use the standard normal distribution table to find the value of the z-score that corresponds to the 95th percentile. This value is approximately 1.645.

Now, we can use the formula for the normal distribution to find the tire life value that corresponds to the z-score of 1.645. This formula is:

X = μ + zσ

Where X is the tire life value, μ is the mean of the distribution (65,000 miles), z is the z-score (1.645), and σ is the standard deviation of the distribution (1500 miles).

Plugging in the values, we get:

X = 65,000 + 1.645(1500)

X = 67,467.5

This means that 95% of the tires will have a life of at least 67,467.5 miles.

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Answer: y = 14.50x + 2.99

Step-by-step explanation:

The equation is y = mx + b

y is the total cost and x is the number of shirt

We know each shirt is $14.50, and she bought x shirts, so 14.50 is the slope

The 2.99 shipping fee is the y-intercept

So our equation is

y = 14.50x + 2.99

Answer:

Step-by-step explanation:

The answers that  best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.

The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.

To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.

Therefore the correct option is C.

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Answer:

See Explanation

Step by step Explanation:

The question is incomplete as the plots that show the distance traveled is not given.

So, I will answer the question with the attached plots.

The number of dots on each day represents the number of miles travelled on that day.

From Elizabeth's plot, the shortest is 1 mile on day 4 (i.e. 1 dot on day 4)

From Izak's plot, the shortest is 2 miles on day 3 (i.e. 2 dots on day 3)

Calculate the difference between both distances

\(d = 2\ miles - 1\ mile\)

\(d = 1\ mile\)

Hence, the shortest distance travelled by Izak is 1 mile more than the shortest by Elizabeth

Answer:

Step-by-step explanation: