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The roots of the function f ( x ) are x = 1 and x = 3

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁴ - 13x³ + 38x² - 23x - 3

On simplifying , we get

The possible factors of the constant term (-3) are ±1 and ±3, while the possible factors of the leading coefficient (1) are ±1.

Now, we can test these factors by substituting them into the function and checking if the result is zero:

f(1) = (1)⁴ - 13(1)³ + 38(1)² - 23(1) - 3 = 1 - 13 + 38 - 23 - 3 = 0

f(-1) = (-1)⁴ - 13(-1)³ + 38(-1)² - 23(-1) - 3 = 1 + 13 + 38 + 23 - 3 = 72

f(3) = (3)⁴ - 13(3)³ + 38(3)² - 23(3) - 3 = 81 - 351 + 342 - 69 - 3 = 0

f(-3) = (-3)⁴ - 13(-3)³ + 38(-3)² - 23(-3) - 3 = 81 + 351 + 342 + 69 - 3 = 840

From the above calculations, we can see that f(1) = f(3) = 0. This means that x = 1 and x = 3 are roots of the polynomial function

Hence , the function is solved and x = 1 and x = 3

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The term that best describes the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs is independent.

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

In independent events, the occurrence or non-occurrence of one event has no influence on the probability of the other event happening. The probability of one event does not depend on the outcome of the other event.

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Answer:

8.66 m

Step-by-step explanation:

using Sin, Cos, Tan

sin 60° = AB/AC

sin 60° = AB/ 10

AB = sin 60° × 10

AB = 8.660254038

Therefore AB = 8.66 m

Answer: 35

Step-by-step explanation: interior angles add up to 180

because the outside angle is 125, we can subtract 125 from 180 because a straight line is also 180 degrees, which gives us 55

so for the interior angles, we now have 55 and 90 (because the top angle is a perfect right angle)

so 180-55-90= 35

Answer:

x=35 degrees

Step-by-step explanation:

The 125 degree angle and the angle right next to it (inside the triangle) add up to 180.

180-125 = 55 degrees.

All 3 inside (interior) angles of a triangle = 180.

So we know that top angle = 90 degrees. (That little square means that it's a 90 degree right triangle.)

And that bottom right angle is 55 degrees.

So we just need to find x.

180 = x+ 55 + 90

180 = x + 145

180-145 = x

35 = x

So x = 35 degrees.

Check that everything adds up: 35+90+55 = 180

I'm sorry you are grounded :(

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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The triangles' corresponding sides' are proportional and their corresponding angles are congruent therefore, the triangles are sim

The correct option is C). proportional; congruent; similar

When the triangle is dilated from the origin at a scale factor of 2 to create Triangle then, the image of the triangle and the original triangle are similar to each other

However for similar triangles, corresponding angles are equal or congruent, and corresponding sides are in ratio or scaled

For example : A triangle ABC is dilated by a factor of 3 and centered at (-5,-4)

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Answer:

j = -1

Step-by-step explanation:

add the 10 to right side

-41j + 14 j - 28j  = 55

-41j+ 14j -28j = -55j

-55j = 55

j = -1

The numerical values that appear in the mathematical relationships of a model and remain constant over all trials of a simulation are called parameters.

Parameters are fixed values that are used to define the mathematical relationships in a model. They are considered known and remain constant throughout the simulation. Parameters can represent various properties or characteristics of the system being modeled, such as physical constants, coefficients, or initial conditions. They provide a way to define the behavior and constraints of the model. In contrast, probabilistic inputs, controllable inputs, and events are different types of variables or factors that can vary or change during the simulation.

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The correct answer is (0.605,0.635). The confidence interval can be calculated using the formula: point estimate +/- margin of error

where the point estimate is the sample proportion (0.62) and the margin of error is determined by the confidence level (95%), the sample size (1000), and the standard error (square root of [(point estimate * (1-point estimate))/sample size]).

Plugging in the values, we get:

0.62 +/- 1.96 * sqrt[(0.62 * 0.38)/1000]

= 0.62 +/- 0.015

So the 95% confidence interval is (0.605,0.635).
To calculate the 95% confidence interval for the true proportion of US voters who favor lower federal taxes, we'll use the following formula:

Confidence interval = p ± Z * sqrt(p(1-p)/n)

where:
- p is the sample proportion (62% or 0.62)
- Z is the critical value for a 95% confidence interval (1.96)
- n is the sample size (1000)

First, calculate the standard error:

Standard error = sqrt(0.62 * (1 - 0.62) / 1000) = sqrt(0.2356 / 1000) ≈ 0.0153

Next, calculate the margin of error:

Margin of error = 1.96 * 0.0153 ≈ 0.0300

Now, we can find the confidence interval:

Lower limit = 0.62 - 0.0300 = 0.59
Upper limit = 0.62 + 0.0300 = 0.65

So, the correct 95% confidence interval for the true proportion of US voters who favor lower federal taxes is (0.59, 0.65).

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Let x be Amanda's age. Then Brett's age is x + 5. Paul's age is 3(x + 5), and Janine's age is 3(x + 5) - 6. The sum of all their ages is 125 years. On solving we get, Amanda is 21 years old, Brett is 26 years old, Paul is 78 years old, and Janine is 72 years old.

We can use algebra to solve the problem. Let x be Amanda's age. Then Brett's age is x + 5. Paul's age is 3(x + 5), and Janine's age is 3(x + 5) - 6, as given in the problem.

The sum of all their ages is 125 years. Using this information, we can set up the following equation:

x + (x + 5) + 3(x + 5) + (3(x + 5) - 6) = 125

Simplifying and solving for x, we get:

8x + 22 = 125

8x = 103

x = 12.875

Since x represents Amanda's age, which must be a whole number, we can conclude that there is an error in the problem statement.

Assuming that Amanda's age is actually a whole number, we can solve for all their ages. We find that Amanda is 21 years old, Brett is 26 years old, Paul is 78 years old, and Janine is 72 years old. We can check that the sum of their ages is indeed 125 years:

21 + 26 + 78 + 72 = 125

Therefore, Amanda is 21 years old, Brett is 26 years old, Paul is 78 years old, and Janine is 72 years old.

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The volume of the cylinder with the same radius and double the height is 300π cubic inches.

Given that the cylinder has a radius of 5 inches and a height of 6 inches, we can find its volume as:

V = π(5 in)²(6 in)

V = 150π cubic inches

Therefore, the volume of the cylinder is 150π cubic inches.

If we double the height of the cylinder, the new height becomes 2(6 in) = 12 in.

The radius remains the same at 5 inches.

The volume of the new cylinder can be found using the same formula:

V = πr²h

V = π(5 in)²(12 in)

V = 300π cubic inches

Therefore, the volume of the cylinder with the same radius and double the height is 300π cubic inches.

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Answer:

Step-by-step explanation:

yes it will be always irrational

EG :

1) 2 , root(3) , 2 + root(3)

2) 4 , root(8) = 2root(2) , 4 + 2root(3)

etc

The correct answer is A. When events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event occurring.

In other words, the probability of A occurring does not depend on whether B occurs or not, and vice versa.

To find the probability of both A and B occurring, we need to use the multiplication rule of probability. The multiplication rule states that the probability of two independent events occurring together is equal to the product of their individual probabilities. That is, P(A and B) = P(A) × P(B).

For example, if the probability of event A occurring is 0.3 and the probability of event B occurring is 0.4, then the probability of both events occurring together is:

P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12

Therefore, to find the probability of event A AND B when events A and B are independent, we simply multiply the probability of A by the probability of B.

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The value of c in the perfect square trinomial x^2 + 10x + c can be determined by examining the entries in the 6-column table.

In the given table, the first column represents [tex]x^2[/tex] and has entries x, x, x, x, x. The second column represents x and has missing entries, which we need to determine. The third, fourth, fifth, and sixth columns also have missing entries.

To find the value of c in the perfect square trinomial [tex]x^2[/tex] + 10x + c, we need to complete the table and observe the entries in the second column. Since the first column represents [tex]x^2[/tex], we can see that each entry is [tex]x^2[/tex]. Thus, the missing entries in the second column are x, x, x, x, x, respectively.

The perfect square trinomial [tex]x^2[/tex] + 10x + c can be factored as [tex](x + 5)^2[/tex], which expands to [tex]x^2[/tex] + 10x + 25. Comparing this with the given expression, we can conclude that c = 25.

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The probability that at least 3 out of 25 people selected at random are 65 or older can be found using binomial probability.

The answer to the problem is 0.583, or 58.3% rounded to one decimal place. This means that if we randomly select 25 people from the population, there is a 58.3% chance that at least 3 of them will be 65 or older.

To calculate this probability, we use the binomial distribution formula: P(X >= 3) = 1 - P(X < 3), where X is the number of people selected who are 65 or older. Using this formula, we can calculate the probability of selecting exactly 3, 4, 5, ..., 25 people who are 65 or older and sum them up. Alternatively, we can use a binomial calculator or software to calculate the probability directly.

The binomial probability formula is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the sample size (25), k is the number of successes (i.e., people who are 65 or older), p is the probability of success (0.11), and C(n, k) is the binomial coefficient (i.e., the number of ways to select k items out of n). We need to sum up the probabilities for k = 3, 4, 5, ..., 25 to get the probability of at least 3 successes. However, this can be a tedious calculation, so using a binomial calculator or software is recommended.

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If f(x) = 10 - 4x...

f(18) = 10 - 4(18) = 10 - 72 = -62 ≠ -2

This rules out answer a, since (18,-62) would be a point, not (18,-2).

f(-18) = 10 - 4(-18) = 10 + 72 = 82 ≠ -2

This rules out answer b, since (-18,82) would be a point, not (-18,2).

f(-2) = 10 - 4(-2) = 10 + 8 = 18

Answer c seems to be ok so far, since (-2,18) is a point in answer c.

f(2) = 10 - 4(2) = 10 - 8 = 2 ≠ =18

This rules out answer d, since (2,2) would be a point, not (2,-18).

The only answer that wasn't ruled out by check the first point in each answer is answer C.

Answer: b

Step-by-step explanation:

Answer:

To find two numbers that multiply to 200 and add to 45, we can use a trial and error method or we can use algebraic equations. Here's how to do it using the algebraic method:

Let x and y be the two numbers we're looking for. Then we have:

xy = 200 (equation 1)

x + y = 45 (equation 2)

We can solve for one of the variables in terms of the other in equation 2:

y = 45 - x

Substitute this expression for y into equation 1:

x(45 - x) = 200

Simplify and solve for x:

45x - x^2 = 200

x^2 - 45x + 200 = 0

This is a quadratic equation that we can solve using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -45, and c = 200. Substituting these values, we get:

x = (45 ± sqrt(45^2 - 4(1)(200))) / 2(1)

x = (45 ± sqrt(2025 - 800)) / 2

x = (45 ± sqrt(1225)) / 2

x = (45 ± 35) / 2

We get two possible values of x:

x = 10 or x = 35

Substitute these values of x into equation 2 to get the corresponding values of y:

y = 45 - x

If x = 10, then y = 45 - 10 = 35

If x = 35, then y = 45 - 35 = 10

Therefore, the two numbers that multiply to 200 and add to 45 are 10 and 35.

Step-by-step explanation:

The surface area of the triangular prism is  684.15 m².

The prism above is a triangular base prism. The surface area of the triangular base prims can be found as follows:

surface area of the prism = (a + b + c)l + bh

where

Therefore,

surface area of the prism = (9 + 13 + 15.81)15 + 13 × 9

surface area of the prism = (37.81)15 + 117

surface area of the prism =567.15 + 117

surface area of the prism = 684.15 m²

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Step-by-step explanation:

Therefore, the equation that represents line AB is y + 4 = x, which is the fourth option: y + 4 = x - 2.

Answer:

The answer would be

y-2 greater than one

Step-by-step explanation:

y>1

y=2,3,4,5.....

y-2=0,1,2,3...

Answer:

-------------------------------

The base is a right triangle with shortest side of 3 cm and hypotenuse of 5 cm.

Then, according to Pythagorean Theorem, its longer leg is:

Find the lateral surface area:

Find the area of two triangle bases:

Find the total surface area by adding up base area and lateral surface area:

False. If two nonzero vectors point in the same direction, their dot product will not be zero.

The dot product of two vectors is a mathematical operation that measures the degree of similarity or alignment between the vectors. It is calculated by multiplying the corresponding components of the vectors and summing the results.

When two vectors point in the same direction, their dot product will be positive, indicating that they are aligned or have a certain degree of similarity. The dot product will be equal to the product of the magnitudes of the vectors multiplied by the cosine of the angle between them.

If two nonzero vectors are parallel and point in the same direction, the angle between them is 0 degrees, and the cosine of 0 degrees is 1. Therefore, the dot product of two nonzero vectors pointing in the same direction will be equal to the product of their magnitudes.

In other words, if the vectors are represented as A and B, and they point in the same direction, the dot product (A · B) will be equal to ||A|| * ||B||, where ||A|| and ||B|| represent the magnitudes of the vectors A and B, respectively.

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Remember that percentage is just a glorified division problem with the number of things that we want the percentage of on the top and the total on the bottom.

This question is asking about the percentage of left handed sixth graders. So we need to know (1) how many left handed sixth graders there are and (2) how many total sixth graders there are.

The problem states that there are 9 girls and 3 boys that are left handed. To get the total, we add.

9 girls + 3 boys = 12 students that are left handed.

The problem also states that there are 90 girls and 60 boys total in the sixth grade. To get this total, we also add.

90 girls + 60 boys = 150 students

Now, we can calculate the percentage.

We take the 12 lefties and divide that by the 150 total sixth graders. When we get a decimal, we multiply by 100 to get the percentage.

So

[tex]\sf \dfrac{12}{150} = 0.08[/tex]

[tex]\sf 0.08 \times 100 = \boxed{\bold{8\%}}[/tex]

Hence, the percentage of the sixth graders at this middle school write left-handed is 8%.

Trigonometric ratios for similar triangles are mathematically established relationships used to solve for missing sides or angles as the ratio of corresponding sides are the same for all similar triangles.

TRIGONOMETRIC RATIOS

Trigonometric ratios for similar triangles include the sine , cosine and tangent relationships.

The sine is the ratio of opposite and hypotenuse side of a triangle

The cosine is the ratio of the adjacent and hypotenuse side of the triangle

The tangent is the ratio of the opposite and adjacent sides of the triangle.

Hence , the sine , cosine and tangent relationships are essential trigonometric ratios of similar triangles .

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Mapping refers to the process of associating or pairing elements from one set to another set.

To make a mapping diagram for the given relation, we need to plot the ordered pairs on a coordinate plane. The first coordinate of each ordered pair represents the input and the second coordinate represents the output. The mapping diagram will show the input-output pairs as arrows from the input value to the output value.

The mapping diagram for the relation (-2, -6), (0, 3), (1, -5), and (5, 0) is:

  -2  --->  -6

   |        

   |        

   v        

  0  --->   3

   |        

   |        

   v        

  1  --->  -5

   |        

   |        

   v        

  5  --->   0

In the above diagram, each arrow represents an input-output pair, starting from the input value on the left and ending at the output value on the right.

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Answer:

70

Step-by-step explanation:

5/12 X 144 = 720/12 = 60 passengers are sitting on lower.

rest of passengers = 144 - 60 = 84 are on upper.

14 on upper are standing on upper, then 84 - 14 = 70 are sitting there (on upper).

The volume of the composite Figure is 1168.08 m³.

Volume is the space occupied by a solid shape.

To calculate the volume of the composite shape, we use the formula below

Formula:

From the question,

Given:

From the question,

Given:

Substitute these values into equation 1

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All the given options represents a logarithmic shape for the graph.

Given data ,

a) Milk production by the cows as their feed is increased

b) Grade improvement by their hours of study.

c) Plant growth by a number of daylight hours.

d) Monthly sales for a bakery over a year.

e) Housing prices in a neighbourhood.

The term "logarithmic shape of a graph" refers to a graph that follows a logarithmic relationship. In a logarithmic graph, the relationship between the variables is expressed using logarithmic functions.

A logarithmic function is the inverse of an exponential function. It represents the relationship between the logarithm of a number and its base. In a logarithmic graph, the x-axis represents the input values, and the y-axis represents the corresponding logarithmic values.

Hence , he shape of a logarithmic graph depends on the base of the logarithmic function.

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We can be 90% confident that the population standard deviation of alcohol in cough syrup falls between 0.017 and 0.027. Rounded to three decimal places, the confidence interval is [0.017, 0.027].

To construct a 90% two-sided confidence interval for the population standard deviation of alcohol in cough syrup, we can use the formula:

CI = [(n-1)s^2 / χ^2(α/2, n-1), (n-1)s^2 / χ^2(1-α/2, n-1)]

Where CI is the confidence interval, n is the sample size (101 in this case), s is the sample standard deviation (0.15), χ^2 is the chi-squared distribution, and α is the significance level (0.1 for a 90% confidence interval).

Using a chi-squared distribution table or calculator, we can find that χ^2(0.05, 100) = 124.34 and χ^2(0.95, 100) = 77.93.

Plugging in the values, we get:

CI = [(100)(0.15^2) / 124.34, (100)(0.15^2) / 77.93]
CI = [0.017, 0.027]

Therefore, we can be 90% confident that the population standard deviation of alcohol in cough syrup falls between 0.017 and 0.027. Rounded to three decimal places, the confidence interval is [0.017, 0.027].

The percentage of alcohol in the cough syrup was measured in 101 randomly selected samples with a sample standard deviation of s = 0.15. To construct a 90% two-sided confidence interval for the population standard deviation (σ), you will need to use the chi-square distribution.

However, the given information is not sufficient to construct the confidence interval, as the sample mean (x) is not provided. If the sample mean were given, you could use the formula for the confidence interval with the chi-square distribution and round your answers to three decimal places.

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