The intersection of a right cylinder and a plane makes an oval cross section. Which option is true about the plane of intersection?

1.The right cylinder is cut with a plane that is neither parallel nor perpendicular to the base.

2.The right cylinder is cut with a plane perpendicular to the base and passing through the center.

3.The right cylinder is cut with a plane parallel to the base.

4.The right cylinder is cut with a plane perpendicular to the base but not passing through the center.

The sum of the x-values where f(x) = g(x) is 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 3(2)ˣ

g(x) = 6x

When f(x) = g(x), we have

3(2)ˣ = 6x

Solving for x, we have

x = 1 and x = 2

When these values are added, we have

Sum = 1 + 2

Evaluate

Sum = 3

Hence, the sum of the x-values where f(x) = g(x) is 3

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The first term of an A.P is 14 and the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the A.P is 70/11.

The first term of an A.P is 14. Let the common difference be d. Then the second term of the A.P is given by 14 + d. Similarly, the third term of the A.P is given by 14 + 2d.

The third term of the A.P.Solution:

Sum of the first 5 terms of the A.P can be expressed as:

5/2 [2a + (5 - 1) d] = 5/2 [2(14) + 4d] = 35 + 10d

Sum of the first 10 terms of the A.P can be expressed as:

10/2 [2a + (10 - 1) d] = 10/2 [2(14) + 9d] = 70 + 45d

According to the question, the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. It can be written as follows: 35 + 10d = - (70 + 45d)

Simplifying the above equation, we get:

55d = -105⇒ d = -105/55 = -21/11

Substituting the value of d in 14 + 2d, we get:

14 + 2d = 14 + 2(-21/11) = 14 - 42/11= 112/11 - 42/11= 70/11

Hence, the third term of the A.P is 70/11.

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The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.

To find the angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12), follow these steps:
Step 1: Determine the coordinates of the given point. In this case, it is (-5, 12).
Step 2: Calculate the horizontal (x) and vertical (y) distances from the origin (0, 0) to the point. The horizontal distance is -5 and the vertical distance is 12.
Step 3: Calculate the angle using the arctangent function (tan^(-1)). The arctangent function takes the ratio of the vertical distance to the horizontal distance as its argument. So, angle = tan^(-1)(12 / -5).
Step 4: Compute the arctangent value using a calculator or an online tool. Angle ≈ tan^(-1)(-2.4) ≈ -67.38 degrees.
Step 5: Convert the angle to a positive value measured counterclockwise from the positive x-axis. Since the angle is measured in the second quadrant, subtract the angle from 180 degrees: 180 - 67.38 ≈ 112.62 degrees.
The angle measured counterclockwise from the positive x-axis to the ray through the point (-5, 12) is approximately 112.62 degrees.

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Answer:

(-0.8, 2.2)

Step-by-step explanation:

Where the two lines intersect is the solution to the System of Equations.

Answer:

the answer would be (-0.8, 2.2) since it hasn't hit -3 yet and if it were to be -1 it would be in the bottom left

Answer: 6 cups

Step-by-step explanation:

Answer:

r≈19.1cm

Step-by-step explanation:

Using the formula

C=2πr

Solving forr

r=C

2π=120

2·π≈19.09859cm

Hope this helps

Therefore, the polynomial that passes through the given points is: f(x) = 6 - 38x - 6x^2 + 4x^3 + 3x^4.

To find the polynomial that passes through the given points, we can use the method of interpolation. Since we have five points, we can use a fourth-degree polynomial to fit the data.

Let's assume that the polynomial is of the form:

f(x) = a0 + a1x + a2x^2 + a3x^3 + a4x^4

We can find the coefficients a0, a1, a2, a3, and a4 by substituting the given points into the equation and solving the resulting system of linear equations.

Substituting (-4, 89) into the equation, we get:

89 = a0 - 4a1 + 16a2 - 64a3 + 256a4

Substituting (-3, 7) into the equation, we get:

7 = a0 - 3a1 + 9a2 - 27a3 + 81a4

Substituting (-1, -1) into the equation, we get:

-1 = a0 - a1 + a2 - a3 + a4

Substituting (1, -1) into the equation, we get:

-1 = a0 + a1 + a2 + a3 + a4

Substituting (4, 329) into the equation, we get:

329 = a0 + 4a1 + 16a2 + 64a3 + 256a4

Now we have five linear equations with five unknowns, which we can solve using any method of linear algebra. One possible way is to use matrix inversion. After solving for the coefficients, we get:

a0 = 6

a1 = -38

a2 = -6

a3 = 4

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There is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.

The null hypothesis is that the true proportion of blocks that contain gold is equal to 0.20. The alternative hypothesis is that the true proportion of blocks that contain gold is less than 0.20.

The test statistic is calculated as follows:

z = (p - p₀) / √(p₀(1-p₀) / n)

The test statistic is equal to -2.00.

The p-value is calculated as follows:

p-value = 2 * P(Z < -2.00)

The p-value is equal to 0.0477.

Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Therefore, there is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.

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Answer:

a) It would have taken 1 person 14 days to do this amount of work.

b) It would take 1 person 56 days to finish building this house extension.

We know that 1 person can build a house extension in 70 days. This means that in 1 day, 1 person can do 1/70 of the work. In 7 days, 2 people can do 2 * 7 * 1/70 = 2/10 of the work. This means that 1 person can do 1/10 of the work in 7 days. To finish the remaining 8/10 of the work, 1 person would need 7 * 8 = 56 days.

Step-by-step explanation:

Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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Answer:

3 ways

Step-by-step explanation:

Using the arrows that they gave us, (which are the directions). The only possible ways are 3. Which I have shown in the screenshot attached below.

If we were to try to do it another time using the directions, it wouldn't work and we would most likely skip a step

Hope I helped!

Answer:

A, C

Step-by-step explanation:

For A, it's correct because they both start with 865.4, but the number in the problem has numbers after the 4, so A is right. B, is not because they both have 865.47, but the one in the problem has a 3, and C has 5, so no. C, is right, because the the problem's thousandths place is greater than C's. D, is not, because it's ones place is greater than the original number.

Answer:

the answer is lateral area

In the chi-square test expected frequencies represent The frequencies one would expect if the null hypothesis were true

The expected frequencies in the chi-square test represent the frequencies one would expect if the null hypothesis were true. This means that the expected frequencies are calculated based on the assumption that there is no significant difference between the observed and expected frequencies, as suggested by the null hypothesis. The chi-square test compares the observed frequencies with the expected frequencies to determine if there is a significant association or difference between the variables being studied.

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To convert the vertex form of a quadratic equation to standard form, we need to expand the squared term and simplify the expression.

Starting with the vertex form of the equation of a parabola:

y = 2(x - 3)^2 + 5

We can expand the squared term using the square of a binomial formula:

y = 2(x^2 - 6x + 9) + 5

Next, we distribute the coefficient 2:

y = 2x^2 - 12x + 18 + 5

Simplifying the constant terms:

y = 2x^2 - 12x + 23

This is the standard form of the equation of the parabola.

To find the dimensions of the rectangle, we need to use Cramer's rule, which is a method for solving systems of linear equations.

   Let's start by defining the variables:

Let x be the width of the rectangle in cm.

Let y be the length of the rectangle in cm.

According to the problem, we have two equations:

y = 3x - 6 (the length is 6cm less than three times the width)

2(x + y) = P (the perimeter of the rectangle is P)

We can rewrite the second equation as:

2x + 2y = P

To solve for x and y, we need to set up a matrix and apply Cramer's rule. The matrix is:

| 0 1 | | x | | -6 |

| 2 2 | x | y | = | P |

Using Cramer's rule, we can solve for x and y as follows:

x = (|-6 1| / |-2 1|) = 9

y = (|0 -6| / |-2 1|) = 12

Therefore, the width of the rectangle is 9 cm and the length of the rectangle is 12 cm.

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To find the probability of selecting either a Red or a Brown almond M&M, we need to add their respective probabilities. The probability of selecting either a red or brown almond M&M is 0.2 or 20%.

P(R or Br) = P(R) + P(Br)

From the table given, we know that the probability of selecting a Red almond M&M is 0.1 and the probability of selecting a Brown almond M&M is also 0.1. Therefore,

P(R or Br) = 0.1 + 0.1 = 0.2

So, the probability of selecting either a Red or a Brown almond M&M is 0.2 or 20%.

In summary, to find the probability of selecting either one event or another event, we add their probabilities together. In this case, the probability of selecting a Red or a Brown almond M&M is 0.2 or 20%.

To find the probability of selecting either a red (R) or brown (Br) almond M&M, you can simply add the individual probabilities for each color since they are mutually exclusive events (selecting one does not affect the other).

According to the given probability distribution, the probability of selecting a red M&M (R) is 0.1, and the probability of selecting a brown M&M (Br) is 0.1.

So, to find the probability of selecting either a red or brown M&M (P(R or Br)), you can use the formula:

P(R or Br) = P(R) + P(Br)

Plugging in the given probabilities:

P(R or Br) = 0.1 (for R) + 0.1 (for Br)

P(R or Br) = 0.2

So, the probability of selecting either a red or brown almond M&M is 0.2 or 20%.

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The sampling design used in this scenario is cluster sampling.

Cluster sampling involves dividing the population into groups or clusters (in this case, the 15 towns) and randomly selecting entire clusters to be included in the sample. In this case, the intern randomly selected 20 customers from each town, which means that the clusters were the towns themselves.

Cluster sampling is a practical and efficient sampling method when it is difficult or expensive to access individual elements of the population. By selecting entire clusters, the sampling process becomes more manageable, and it can reduce costs and logistical challenges.

However, it's important to note that cluster sampling introduces the possibility of within-cluster similarity, meaning that individuals within the same cluster may have similar characteristics or behaviors. This can affect the variability of the sample and the generalizability of the findings to the entire population. It is important to consider this potential bias and account for it in the data analysis and interpretation.

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To compute the trimmed mean for the given data, we need to first delete the smallest and largest observed values, which are 0.76 and 0.96 respectively. Then we calculate the mean of the remaining 28 values.

The trimmed data set after deleting the smallest and largest values is:

0.81 0.88 0.82 0.90 0.84 0.84 0.91 0.94 0.86 0.86 0.88 0.87 0.89 0.91 0.86 0.87 0.88 0.83 0.91 0.91 0.86 0.89 0.84 0.88 0.88 0.89 0.83 0.90 0.88 0.92 0.85 0.84 0.86

The sum of these values is 24.39, and the trimmed mean is 24.39/28 = 0.871 (rounded to three decimal places).

The trimmed mean is considered to be a resistant measure of central tendency because it is less affected by extreme values compared to the mean. In this case, even though we deleted the smallest and largest values, the resulting trimmed mean is very close to the mean of the original data set (which is 0.8716). Therefore, the trimmed mean is resistant to changes in extreme values in the given data.

The answer is (b) yes, because changing the extreme values does not change the trimmed mean.

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To determine the order in which Harry Potter should visit the 4 places and return to Gryffindor in the least amount of time, we need to look at the graph provided by Hermione.

We can start by looking for the shortest distances between each location. Once we have identified the shortest distances, we can then use this information to determine the most efficient order for Harry to visit each place.
It's important to note that there may be multiple routes that Harry can take to visit all 4 places, but we want to find the one that will take the least amount of time. To do this, we can start by identifying the shortest distance between two locations and continue to do this until we have identified the shortest path to all 4 locations.
Once we have determined the order in which Harry should visit each location, we can then calculate the amount of time it will take for him to travel between each place and return to Gryffindor. This will give us a total time for the entire journey.
We can say that determining the most efficient route for Harry to visit the 4 places and return to Gryffindor in the least amount of time requires careful analysis of the graph provided by Hermione. By identifying the shortest distance between each location and using this information to create the most efficient route, we can minimize the amount of time Harry spends traveling between each place. Once we have identified the order in which Harry should visit each location, we can then calculate the amount of time it will take him to travel between each place and return to Gryffindor. By doing this, we can determine the total amount of time it will take for Harry to complete his journey.

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The equation for finding amount of daily pay is bus-driver gets paid $100 each day plus $0.20 per kilometer, "k" is p = 100 + 0.20k.

The equation for finding the amount of daily pay, "p", in the given situation would be : p = 100 + 0.20k,

In this equation, "p" represents the total daily-pay, "100" is the fixed amount paid each day, and

"$0.20" is the rate per kilometer. "k" represents the number of kilometers driven on that day.

To calculate the daily pay, you add the fixed amount of $100 to the product of the rate per kilometer and the number of kilometers driven on that day.

Therefore, the required equation is p = 100 + 0.20k.

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The given question is incomplete, the complete question is

Write an equation for finding the amount of daily pay, p, in the following situation: A bus driver gets paid $100 each day plus $0.20 per kilometer, "k".

Answer:

Step-by-step explanation:

The transformation for the function g(x) = 5ˣ - 2 involves a vertical shift downward by 2 units compared to the parent function f(x) = 5ˣ. This is because the constant term (-2) is subtracted from the function. So, the graph of g(x) will be identical to the graph of f(x), except that it will be shifted downward by 2 units. Specifically, the point (0, 1) on the graph of f(x) will be shifted down to (0, -1) on the graph of g(x), and similarly, all other points on the graph will be shifted downward by 2 units.

We can match the terms in the left column to the correct bolded examples as follows:

Sum: 1 + 1 = 2

Difference: 7 - 2 = 5

Term: 2x

Product: 9 * 9 = 81

Factor: 81 ÷ 9 = 9

Quotient: 81 ÷ 9 = 9

Coefficient: 7x - 8y

Variable: 5x + 3

To match the correct expression, an understanding of the mathematical terms is essential. The sum is the addition of terms and in the list, 1 + 1 is an example of a sum. Also, the product is the multiplication of numbers and 9 * 9 = 81 is an example of a product.

Coefficients are numbers that are matched with letters in algebra. A variable is a letter beside a number in an expression. In the option, x is the variable besides 5.

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Answer:

1 cup

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve for the total number of cups used, we need to first convert each fraction to have a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

As of now, each fraction looks like this:

Looking at each of the denominators, we can see that 12 is a multiple of both 4 and 3!

So, let's convert [tex]\frac{1}{3}[/tex].

Now that we have the denominator, we need to multiply the numerator by the same amount, so it stays equivalent.

Now let's convert [tex]\frac{1}{4}[/tex].

4 can be multiplied by 3 to get 12.

1 can be multiplied by 3 to get 3.

Now, each fraction looks like this:

Adding up the numerators:

Adding that back on top of the denominator:

So, [tex]\frac{4}{12}+ \frac{3}{12}+ \frac{5}{12} = \frac{12}{12}[/tex] or 1.

Therefore 1 cup of flour was used that day.

The approximated value of the logarithm expression is 0.5646  + 4log(b)

From the question, we have the following parameters that can be used in our computation:

log, 2≈ 0.3562,

log, 3≈ 0.5646, and

log, 5 ≈ 0.8271

Also, we have

logb (3b⁴)

Using the logarithms property, we have

logb (3b⁴) = logb (3) + log(b⁴)

This gives

logb (3b⁴) = logb (3) + 4log(b)

Substitute the known values in the above equation, so, we have the following representation

logb (3b⁴) = 0.5646  + 4log(b)

Hence, the approximated value is 0.5646  + 4log(b)

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Answer:

  322 in²

Step-by-step explanation:

You want the surface area of the rectangular prism with edge lengths 7 in, 14 in, and 3 in.

The surface area can be computed using the formula ...

  A = 2(LW +H(L +W))

  A = 2(7·14 + 3(7 +14)) = 2(98 +63) = 322

The area of the prism is 322 square inches.

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To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.

Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.

Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.

To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:

d/dx (2πr^3) = 6πr^2 = 0

This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.

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The value of the measure of each sides indicated are:

The measurement of the indicated side can be obtain as illustrated below:

1. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 20 = x / 11

Cross multiply

x = 11 × Tan 20

Value of x = 4

2. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 27 = 5 / x

Cross multiply

x × Sine 27 = 5

Divide both sides by Sine 27

x = 5 / Sine 27

Value of x = 11

3. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 27.2 = 10 / x

Cross multiply

x × Sine 27.2 = 10

Divide both sides by Sine 27.2

x = 10 / Sine 27.2

Value of x = 21.9

4. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 25 = 15 / x

Cross multiply

x × Tan 25 = 15

Divide both sides by Tan 25

x = 15 / Tan 25

Value of x = 32.2

5. The value of x can be obtain as follow:

Cos θ = Adjacent / Hypotenuse

Cos 64 = 4 / x

Cross multiply

x × Cos 64 = 4

Divide both sides by Cos 64

x = 4 / Cos 64

Value of x = 9.1

6. The value of x can be obtain as follow:

Tan θ = Opposite / Adjacent

Tan 33 = x / 14

Cross multiply

x = 14 × Tan 33

Value of x = 9.1

7. The value of x can be obtain as follow:

Sine θ = Opposite / Hypotenuse

Sine 49.6 = 5.6 / x

Cross multiply

x × Sine 49.6 = 5.6

Divide both sides by Sine 49.6

x = 5.6 / Sine 49.6

Value of x = 7.4

8. The value of x can be obtain as follow:

Cos θ = Adjacent / Hypotenuse

Cos 40 = x / 10.2

Cross multiply

x = 10.2 × Cos 40

Value of x = 7.8

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Given 20% of the pupils are girls and the rest are boys. So, there are a total of 1785 pupils in the school.

To solve this problem, we can start by using the information that 20% of the pupils are girls to find the total number of girls and boys in the school. If there are a total of x pupils, then 0.2x are girls and 0.8x are boys.

Next, we can use the fact that the ratio of the number of pupils who wear spectacles to those who do not wear spectacles is 1:5 to find the number of pupils who wear spectacles. Let the number of pupils who wear spectacles be y, then 1/6y are girls who wear spectacles and 5/6y are boys who wear spectacles.

We also know that there is an equal number of girls and boys who wear spectacles, so we can write:

1/6y = 5/6y / 4

where 4 is the ratio of boys to girls who wear spectacles.

Solving for y, we get y = 357 * 24 = 8568. Therefore, the total number of pupils in the school is:

x = 0.2x + 0.8x = 1785

Hence, there are 1785 pupils altogether in the school.

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To find two numbers that multiply to -63 and add to -18, we can start by listing all the factors of -63:

We can see that -9 and 7 are the only two factors that add up to -2.

Therefore, the two numbers that multiply to -63 and add to -18 are -9 and 7.

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