What are the x-intercepts for the graph of y=3(x-1)(x+6)?

1. The set of students who are computer science majors and are taking CSE 191:

\(\( A \cap B \)\)

2. The set of students who are computer science majors but are not taking CSE 191:

\(\( A - B \)\)

3. The set of students who are either computer science majors or are taking CSE 191 (or both):

\(\( A \cup B \)\)

4. The set of students who are neither computer science majors nor taking CSE 191:

\(\( (A \cup B)' \) or \( U - (A \cup B) \)\)  , where U represents the universal set of all students.

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If a sample size is one-fourth the original size, the margin of error will be affected. Specifically, the margin of error will be affected inversely proportional to the square root of the sample size.

Halving the sample size (from the original) will cause the margin of error to increase by a factor of square root of 2, approximately 1.41.

Doubling the sample size (from the original) will cause the margin of error to decrease by a factor of square root of 2, approximately 0.71.

Quadrupling the sample size (from the original) will cause the margin of error to decrease by a factor of square root of 4, approximately 0.5.

Therefore, if the sample size is reduced to one-fourth the original size, the margin of error will be doubled, because the square root of 4 is 2. Conversely, if the sample size is increased fourfold, the margin of error will be halved, because the square root of 1/4 is 1/2.

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On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

The average of the absolute deviations from the center point within a dataset is called the mean absolute deviation. This statistic summarizes the statistical spread or variability. Each data point's average distance from the mean is known as the dataset's mean absolute deviation. This gives a sense of the dataset's variability. To determine the absolute value, take the mean from each integer in the dataset and then subtraction. Take the total of the absolute values next. Subtract the aforementioned sum from the total number of items in the dataset to obtain the mean absolute deviation.

12,12,12,22,23,32,43

Mean Absolute Deviation (MAD): 8.8979591836735

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Answer:

On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735

Step-by-step explanation:

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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The expression 126 \(m^4\) - 63\(m^3\) is equivalent to the given expression                  7m² * (2m -1 )*(m9).

The properties of multiplication are:

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

Here, you should apply the distributive property and power rules for solving this expression and finding an equivalent expression.

First, you should multiply the factors (2m -1)*(9m). As result, you find 18m²-9m.

After that, you should do the product between the previous result (18m²-9m) and the factor 7m². Thus,

(18m²-9m) * 7m²= 126 \(m^4\) - 63\(m^3\).

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Answer:

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

Eliminate y and equate the right sides:

Find y by substitution of the value for x:

The approximate volume of the cone with a radius of 1.75 feet and a height of 2.1 feet is approximately 6.478875 cubic feet.

To calculate the approximate volume of a cone, you can use the formula:

Volume = (1/3) * π * r^2 * h,

where r represents the radius of the cone's base and h represents the height of the cone.

Given that the radius (r) is 1.75 feet and the height (h) is 2.1 feet, we can substitute these values into the formula:

Volume = (1/3) * π * (1.75)^2 * 2.1

To calculate the approximate volume, we'll use the value of π as approximately 3.14:

Volume ≈ (1/3) * 3.14 * (1.75)^2 * 2.1

Now, we can perform the calculations:

Volume ≈ (1/3) * 3.14 * 3.0625 * 2.1

≈ 1.047 * 3.0625 * 2.1

≈ 6.478875

Therefore, the approximate volume of the cone with a radius of 1.75 feet and a height of 2.1 feet is approximately 6.478875 cubic feet.

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The t-distribution is the distribution that uses t-values to establish confidence intervals.t-distribution:

The t-distribution is a probability distribution that is widely used in hypothesis testing and confidence interval estimation. It's also known as the Student's t-distribution, and it's a variation of the normal distribution with heavier tails, which is ideal for working with small samples, low-variance populations, or unknown population variances.The t-distribution is commonly used in hypothesis testing to compare two sample means when the population standard deviation is unknown. When calculating confidence intervals for population means or differences between population means, the t-distribution is also used. The t-distribution is used in statistics when the sample size is small (n < 30) and the population standard deviation is unknown.

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a. The mean is -0.6, the median is 4, and there is no mode in the data set.

b. The range is 15, the variance is 35.2, the standard deviation is approximately 5.93, and the coefficient of variation is approximately -0.988.

c. The Z-scores for the data set are -0.68, -1.69, -0.68, -0.68, and 1.37. There are no outliers as none of the Z-scores exceed the threshold of ±3.

d. The shape of the data set is skewed to the left, indicating a negative skewness.

a. To calculate the mean, we sum up all the values and divide by the sample size:

Mean = (4 - 9 - 4 + 4 + 6) / 5 = -0.6

The median is the middle value when the data is arranged in ascending order:

Median = 4

The mode is the value that appears most frequently, but in this data set, none of the values are repeated, so there is no mode.

b. The range is calculated by finding the difference between the maximum and minimum values:

Range = Maximum value - Minimum value = 6 - (-9) = 15

The variance measures the average squared deviation from the mean:

Variance = ((4 - (-0.6))^2 + (-9 - (-0.6))^2 + (-4 - (-0.6))^2 + (4 - (-0.6))^2 + (6 - (-0.6))^2) / (5 - 1) = 35.2

The standard deviation is the square root of the variance:

Standard Deviation ≈ √35.2 ≈ 5.93

The coefficient of variation is the standard deviation divided by the mean, expressed as a percentage:

Coefficient of Variation ≈ (5.93 / 0.6) × 100 ≈ -0.988

c. The Z-score measures how many standard deviations a data point is away from the mean. To calculate the Z-scores, we subtract the mean from each data point and divide by the standard deviation:

Z1 = (4 - (-0.6)) / 5.93 ≈ -0.68

Z2 = (-9 - (-0.6)) / 5.93 ≈ -1.69

Z3 = (-4 - (-0.6)) / 5.93 ≈ -0.68

Z4 = (4 - (-0.6)) / 5.93 ≈ -0.68

Z5 = (6 - (-0.6)) / 5.93 ≈ 1.37

Since none of the Z-scores exceed the threshold of ±3, there are no outliers in the data set.

d. The shape of the data set can be determined by analyzing the skewness. A negative skewness indicates that the data is skewed to the left, which means that the tail of the distribution extends towards the lower values. In this case, the negative skewness suggests that the data set is skewed to the left.

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= 7a + 3b + 301

Step-by-step explanation:

7a + 5b + 301 - 2b

= 7a + 5b - 2b + 301

= 7a + 3b + 301

To evaluate the integral x^2 dV over the given solid E, we can use cylindrical coordinates. The solid E is bounded by the cylinder x^2 + y^2 = 4, the plane z = 0, and the cone z^2 = 4x^2 + 4y^2. By expressing the integral in cylindrical coordinates, we can calculate the desired value.

In cylindrical coordinates, we can express x, y, and z in terms of the variables ρ, φ, and z. The equation of the cylinder x^2 + y^2 = 4 becomes ρ^2 = 4. The equation of the plane z = 0 remains unchanged, and the equation of the cone z^2 = 4x^2 + 4y^2 can be rewritten as z^2 = 4ρ^2.

To evaluate the integral x^2 dV over the solid E, we need to determine the limits of integration. Since the solid lies within the cylinder x^2 + y^2 = 4, we have ρ ranging from 0 to 2 (since ρ^2 = 4). The angle φ can vary from 0 to 2π, covering the entire circular cross-section of the cylinder. Lastly, z ranges from 0 to the value given by the equation z^2 = 4ρ^2.

Using these limits of integration, we can express the integral x^2 dV in cylindrical coordinates as ∫∫∫ ρ^3 cos^2(φ) dz dρ dφ over the region E. By performing the integration, we can calculate the desired value.

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To the nearest whole number, the probability of rolling a 2 and a 4 is 2.8%.

A 2 rolling up on the first throw has a 1/6 chance of happening. Given that a 2 was rolled on the first throw, the likelihood of rolling a 4 on the second throw is equally 1/6. We will have to multiply the probabilities to get the probability of both the events happening,

= (1/6)x(1/6)

= 1/36.

We get 2.8% after converting to a percentage and rounding to the next full amount. So, the chance of rolling a 2 and then a 4 is found to be 2.8% chance.

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Answer:

47

Step-by-step explanation:

since each gallon is 4 quarts you would multiply by 11. 44 quarts then add 3 extra quarts to get 47

Jeremy used 47 quarts of water to water his garden.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Jeremy used 11 gallons and 3 quarts of water to water his garden

First, we need to convert the gallons to quarts because we are looking for the answer in quarts.

1 gallon = 4 quarts

So, 11 gallons = 11 x 4 = 44 quarts

Now, we need to add the 3 quarts to get the total amount of water used:

44 quarts + 3 quarts = 47 quarts

Jeremy used 47 quarts of water to water his garden.

Hence, Jeremy used 47 quarts of water to water his garden.

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The Wronskian of the given vector functions is \(5t^2-t\). So the option e is correct.

In the given question, we have to find the Wronskian of the following vector functions:

\(u(t) = \left [ \begin{matrix}3t - 1\\ -2t\end{matrix} \right ]\)  and \(u(t) = \left [ \begin{matrix}-2t + 1\\ 3t\end{matrix} \right ]\)

Thomas Muir gave the Wronskian determinant its name after Józef Hoene-Wroski introduced it in 1812. It is applied to the study of differential equations, and in some cases, it can reveal linear independence among a group of solutions.

Wronskian vector functions = \(\left | \begin{matrix}3t - 1 & -2t\\ -2t + 1 & 3t\end{matrix} \right |\)

Now solving the vector

Wronskian vector functions = (3t-1)3t - (-2t)(-2t+1)

Wronskian vector functions = \(9t^2-3t + 2t(-2t+1)\)

Wronskian vector functions = \(9t^2-3t -4t^2+2t\)

Wronskian vector functions = \(5t^2-t\)

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A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through two points, (x₁, y₁) and (x₂, y₂), then we can write the slope as:

a = (y₂ - y₁)/(x₂ - x₁).

Also, for a given line:

y = m*x + s

A perpendicular line to that one must have a slope:

a = -(1/m)

And the intersection between two perpendicular lines forms four 90° angles.

So first, we need to find the slope of the line that passes through A and B.

A = (-3, 3)

B = (-1, -1)

Then the slope of the line is:

a = (-1 - 3)/(-1 - (-3)) = -4/2 = -2

a = -2

The slope of a perpendicular line should be:

slope = -(1/a) = -(1/-2) = 1/2

Then the perpendicular line will be something like:

y = (1/2)*x + b

To find the value of b, we can use the other restriction.

This line needs to pass through point C.

And we can see that point C is:

C = (1, 2)

This means that when x is equal to 1, y must be equal to 2.

Then replacing these in the above equation we get:

2 = (1/2)*1 + b

2 = 1/2 + b

2 - 1/2 = 4/2 - 1/2 = 3/2 = b

Then our equation is:

y = (1/2)*x+ 3/2

The graph of this line can be seen in the image below, the green line is the line that we found.

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Answer:

Step-by-step explanation:

Answer:

x-6/5

Step-by-step explanation:

Two events are mutually exclusive if the probability of their intersection is 0 and they have no sample points in common. Hence, option D is the correct answer.

The two events are called mutually exclusive when they have no sample points in common. Thus, the probability of event A and event B happening is zero. this means that their intersection set is the empty set.

let us take an example-

Let A be a set of odd numbers and B be a set of even numbers.

A = {1,3,5,7,9}

B = {0,2,4,6,8}

A ∩ B = { }

Hence, the two sets - A and B are mutually exclusive of each other.

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The completed table shows the products of each term. we get

       |  2z  |  -4

____________________

22²       | 44z² |

__________|______|______

3zy       | 6zy  | -12z

__________|______|______

-2y²      | -4y² | 8y²

To use the box method for multiplying the two expressions, let's create a table with the terms of each expression:

         |  2z  |  -4

____________________

22²       |

__________|______|______

3zy       |

__________|______|______

-2y²      |

Now, we will multiply each term from the first expression with each term from the second expression and fill in the table:

         |  2z  |  -4

____________________

22²       | 44z² |

__________|______|______

3zy       | 6zy  | -12z

__________|______|______

-2y²      | -4y² | 8y²

The completed table shows the products of each term.

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Answer:

earplugs

Step-by-step explanation:

Because sound waves absorb most sound, the sound is coming from the earplugs which creates the most sound waves rather than water, tissue paper, and air.

Answer:

Water

Step-by-step explanation:

The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.

To solve for the predicted number of runs, we can use the following steps:

Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.

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Answer:

The slope of the line. otherwise known as the gradient, can be found in the equation as the number in front of the x term.

In this case, it is - 1/2 (or -0.5, however you want to answer it)

Answer:

36

Step-by-step explanation:

200-20=180

180/5=36

Step-by-step explanation:

Principal:- $5000

Rate= 8%

Time = 9 years

Interest = P×R×T/100

= 500×8×9/100

= 5×8×9

= 40×9

= 360

Hence, Interest = $360.

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Answer:

B, AC = 2AB

Step-by-step explanation:

C is the mid point of AB so we have:

AC = CB = 1/2 AB

AC + CB = AB

Answer:

\(C=20+0.20N\)

Step-by-step explanation:

Fixed monthly fee = $20

Amount charged per minute for long distance calls = $0.20

\(C\) denotes total cost such that \(N\) minutes are used for long distance calls.

Amount charged for \(N\) minutes for long distance calls \(=0.20N\)

Therefore, an equation for the total cost, C, when N minutes are used for long distance calls is \(C=20+0.20N\)

Answer:

3 cm

Step-by-step explanation:

The probability that this batter will hit a home run on this pitcher's next pitch is approximately 0.074, or 7.4%.

To determine the probability that the batter will hit a home run on the pitcher's next pitch,

we need to consider the probabilities of the pitcher throwing a fastball and a curveball, as well as the probabilities of hitting a home run on each type of pitch.

Given that the pitcher throws fastballs 80% of the time and curveballs 20% of the time, we can calculate the probability of the batter facing each type of pitch:

- Probability of facing a fastball = 80% = 0.8
- Probability of facing a curveball = 20% = 0.2

Now, we need to determine the probability of hitting a home run on each type of pitch:

- Probability of hitting a home run on a fastball = 8% = 0.08
- Probability of hitting a home run on a curveball = 5% = 0.05

To find the overall probability of hitting a home run on the pitcher's next pitch, we can use the following formula:

Overall probability = (Probability of facing a fastball * Probability of hitting a home run on a fastball) + (Probability of facing a curveball * Probability of hitting a home run on a curveball)

Plugging in the values we have:

Overall probability = (0.8 * 0.08) + (0.2 * 0.05)
Overall probability = 0.064 + 0.01
Overall probability = 0.074

Therefore, the probability that this batter will hit a home run on this pitcher's next pitch is approximately 0.074, or 7.4%.

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Step-by-step explanation: Multiple of 3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99. multiple of 4: 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96. therefore, first three common multiples between 3 and 4 12,24,36.

The state income tax owed on a $90,000 per year salary is $5,175.

Tax is a compulsory amount that is levied by the government on the income of individuals or on certain goods and services. Progressive tax is when the amount of tax paid by individuals increases as the amount of income earned increases. The amount paid as tax can be determined by multiplying the appropriate tax rate by the total income.

Tax paid = income x tax rate

$90,000 x 5.75%

$90,000 x 0.0575 = $5,175

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The state income tax owed on an $90,000 per year salary is  $5,175.

Taxes are mandatory contributions levied on individuals or corporations by a government entity

Given,

A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 3000 2% 3001 - 5000 3% 5001 - 17,000 5% 17,001 and up 5.75%

We need to find the state income tax owed on an $90,000 per year salary.

Tax paid = income x tax rate

$90,000 x 5.75%

5.75% should be converted to decimal by dividing with 100.

5.75/100=0.0575

So $90,000 x 0.0575 = $5,175

Hence the state income tax owed on an $90,000 per year salary is  $5,175.

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