two points are selected randomly on a line of length 18 so as to be on opposite sides of the midpoint of the line. in other words, the two points x and y are independent random variables such that x is uniformly distributed over [0,9) and y is uniformly distributed over (9,18] . find the probability that the distance between the two points is greater than 7 . answer:

The gardener used 40.5 gallons of gasoline in his lawn mowers in the one month.

Let's say the amount of gasoline used in the lawn mowers is x gallons.

Then, the rest of the gasoline (61.5 - x) would have been used for other purposes.

Since the total amount of gasoline used is 61.5 gallons, we can set up an equation:

x + (61.5 - x) = 61.5

Simplifying this equation, we get:

x + 61.5 - x = 61.5

Combining like terms, we get:

61.5 = 61.5

This equation is true, so we know that our assumption that x is the amount of gasoline used in the lawn mowers is correct.

Therefore, the gardener used x = 40.5 gallons of gasoline in his lawn mowers in the one month.

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Answer:The 25 percent of 1000 is equal to 250. It can be easily calculated by dividing 25 by 100 and multiplying the answer with 1000 to get 250.

Step-by-step explanation:

Answer:

$1,593

Step-by-step explanation:

I=PRT

I=$2,276×14%×5

I=1,593.2 to nearest tenth

I=$1,593

The line 13x - 14y = 70 expressed in slope-intercept form is y = (13/14)x - 5.

Here are the steps to follow:

Step 1: Start with the given equation, which is in standard form: 13x - 14y = 70.

Step 2: Solve for y to put it in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept).

First, subtract 13x from both sides of the equation:
-14y = -13x + 70

Next, divide both sides by -14:
y = (13/14)x - 5

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Since 504 > 100, Town A had a greater average rate of change.

The given function is P(x)=10x²+8x+600 represents the population of Town A.

Here, x represent the number of years.

In year 0, Town B had a population of 400 people. Town B's population increased by 100 people each year.

P(x)=400+100x

We can calculate the average rate of change for each town by finding the difference between the population in year 8 and the population in year 4 and dividing by the number of years (4).

For Town A, we have:

P(8) - P(4) = 10(8² + 8(8) + 600 - (10(4²) + 8(4) + 600) = 2016

Average rate of change = 2016/4 = 504

For Town B, we have:

400 + (100×4) = 800

Average rate of change = 400/4 = 100

Since 504 > 100, Town A had a greater average rate of change.

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The probability that the randomly selected point is in the bullseye is: 1/3

We are told that there are two concentric circles.

Now, the circles that have a common centre are referred to as concentric circles and have different radii. In other words, it is defined as two or more circles that have the same centre point. The region between two concentric circles are of different radii is known as an annulus.

Now, the bulls eye diameter of 4 cm since the radius is 2 cm

Meanwhile, the outer part forms a diameter of 8 cm.

Thus:

Probability of hitting the bulls eye = 4/12 = 1/3

Probability of hitting the outer part = 8/12 = 2/3

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Among the given numbers, -0.52 is closer to -1/2, 0.35 is closer to 0, and 0.25 is closer to both 0 and 1/2.

To determine which number is closer to -1/2, 0, and 1/2, we need to find the absolute value of the difference between each number and the three given values, and then compare the results.

- For 0.35: The absolute value of the difference between 0.35 and -1/2 is approximately 0.85, the absolute value of the difference between 0.35 and 0 is 0.35, and the absolute value of the difference between 0.35 and 1/2 is approximately 0.15. Therefore, 0.35 is closer to 0 than to -1/2 or 1/2.

- For -3/5: The absolute value of the difference between -3/5 and -1/2 is approximately 0.05, the absolute value of the difference between -3/5 and 0 is approximately 0.6, and the absolute value of the difference between -3/5 and 1/2 is approximately 0.95. Therefore, -3/5 is closer to 0 than to -1/2 or 1/2.

- For -0.52: The absolute value of the difference between -0.52 and -1/2 is approximately 0.02, the absolute value of the difference between -0.52 and 0 is approximately 0.52, and the absolute value of the difference between -0.52 and 1/2 is approximately 1.02. Therefore, -0.52 is closer to -1/2 than to 0 or 1/2.

- For 0.25: The absolute value of the difference between 0.25 and -1/2 is approximately 0.75, the absolute value of the difference between 0.25 and 0 is 0.25, and the absolute value of the difference between 0.25 and 1/2 is approximately 0.25. Therefore, 0.25 is closer to 0 and 1/2 than to -1/2.

- For 3/5: The absolute value of the difference between 3/5 and -1/2 is approximately 1.15, the absolute value of the difference between 3/5 and 0 is approximately 0.6, and the absolute value of the difference between 3/5 and 1/2 is approximately 0.05. Therefore, 3/5 is closer to 0 than to -1/2 or 1/2.

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The dimension of the space of all diagonal 5x5 matrices is 5. This is because there are 5 diagonal entries in a 5x5 matrix, and each of these entries can be any scalar, making the space spanned by 5 basis vectors.

You didn't provide enough information for part (b) "p 7". Please clarify the question for that part. The dimension of the space of all lower triangular 4x4 matrices is 10. In a lower triangular matrix, all entries above the diagonal are zero. For a 4x4 matrix, there are 4+3+2+1=10 non-zero entries, which can be any scalar, making the space spanned by 10 basis vectors.

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Outliers can affect the performance of the classifier and make it difficult to find a linear decision boundary.

True. The level of significance in statistics refers to the probability of making a Type I error, which is rejecting a true null hypothesis. It is typically denoted as alpha and set by the analyst or researcher prior to conducting a hypothesis test. It is considered the amount of risk that an analyst is willing to take in rejecting a true null hypothesis.

True. Linear separability is the ability to classify data points in a dataset using a linear decision boundary. If a dataset is not linearly separable, it means that a linear boundary cannot accurately classify all the data points. One of the reasons why this may happen is due to experimental errors that lead to errant data points. These outliers can affect the performance of the classifier and make it difficult to find a linear decision boundary.

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The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

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The change in temperature of the charcoal from 180°F to 60°F is equal to a decrease of approximately 2.2 degrees Celsius.

To convert Fahrenheit to Celsius, we can use the formula:

Celsius = (Fahrenheit - 32) × 5/9

We know that the initial temperature of the charcoal was 180°F, and it experienced a temperature drop of 120°F. To find the final temperature in Fahrenheit, we can subtract 120°F from 180°F:

Final temperature in Fahrenheit = 180°F - 120°F = 60°F

Now, we can convert the final temperature from Fahrenheit to Celsius using the formula above:

Celsius = (60°F - 32) × 5/9

Celsius = (28°F) × 5/9

Celsius = -2.2222...

Rounding the result to one decimal place, we get:

Celsius = -2.2 degrees Celsius (approx.)

It's worth noting that the Celsius scale is based on the metric system, which is the standard measurement system used in most countries worldwide. In contrast, the Fahrenheit scale is primarily used in the United States and a few other countries, making it less universal. Understanding how to convert between the two scales is crucial in various scientific, engineering, and technical fields.

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Complete question:

A piece of charcoal that was initially at 180°F experiences a temperature drop of 120°F. Express this change of temperature in Celsius degrees.

For a matrix, [tex]A = \begin{bmatrix} 3 & 2& 4 \\ 1& -2& 3\\ 2 &3 &2 \end{bmatrix}\\[/tex]

a) The value of det(M₂₁), det(M₂₂), and det(M₂₃) are -8, -2 and 5 respectively.

b) The values of cofactors of matrix A, A₂₁, A₂₂ and A₂₃ are 8, -2 and -5 respectively.

c) The computed value of determinant, det(A) is equals to -3.

Matrix is a set of elements arranged in rows and columns in order to form a rectangular array. We have a matrix A, defined as [tex]A = \begin{bmatrix} 3 & 2& 4 \\ 1& -2& 3\\ 2 &3 &2 \end{bmatrix}\\[/tex]

We have to determine the following values :

a) The minor of matrix is exist for each element of matrix and is equal to the part of the matrix remained after removing the row and the column containing. First we determine the value Minors and then their determinant. [tex]M_{21} = \begin{bmatrix} 2& 4 \\ 3& 2\\ \end{bmatrix}\\[/tex]

det(M₂₁ ) = | M₂₁ | = 2× 2 - 4× 3 = - 8

[tex]M_{22} = \begin{bmatrix} 3& 4 \\ 2& 2\\ \end{bmatrix}\\[/tex]

det(M₂₂) = | M₂₂| = 2× 3 - 4× 2 = - 2

[tex]M_{23} = \begin{bmatrix} 3& 2 \\ 2& 3\\ \end{bmatrix}\\[/tex]

det(M₂₃ ) = | M₂₃ | = 3×3 - 2×2= 5

b) The value of cofactors of matrix A are A₂₁ = (-1)²⁺¹ M₂₁

= -(-8) = 8

A₂₂ = (-1)²⁺² M₂₂ = -2

A₂₃ = (-)²⁺³ M₂₃ = -5

c) Now, we determine the value of determinant of matrix A from part (b).

det(A) = a₂₁ A₂₁ + a₂₂ A₂₂ + a₂₃ A₂₃

= 1× 8 - 2 (-2) + 3( -5)

= -3

Hence, required value is -3.

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As per the combination method, out of the 400 students surveyed, 380 students chose red as their favorite color.

To solve this problem, we can set up an equation. An equation is a statement that shows the equality between two expressions. In this case, we can write:

(Number of students who chose red) / (Total number of students) = 95/100

We can simplify 95/100 to 0.95. Multiplying both sides of the equation by 400 (the total number of students), we get:

Number of students who chose red = 0.95 * 400

Simplifying the right-hand side of the equation, we get:

Number of students who chose red = 380

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The point V(3, 5) is reflected over the x axis, the new point is V'(3, -5)

Reflection is a type of transformation. Transformation is the movement of a point either up, left, right or down in the coordinate plane.

Reflection is a rigid transformation because it conserves the size and shape of the figure.

If a point A(x, y) is reflected over the x axis, the new point is A'(x, -y)

The coordinate of point V is (3, 5). If the point is reflected over the x axis, the new point is V'(3, -5)

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The 95% confidence interval, we can estimate that the proportion of the entire voting population (p) that prefers Candidate A is between 0.572 and 0.668, expressed as decimals to three places

To estimate the proportion (p) of the entire voting population that prefers Candidate A, we'll use the information provided and calculate the 95% confidence interval. Here are the steps:

1. Calculate the sample proportion (p_hat): Divide the number of people who preferred Candidate A (248) by the total number of people sampled (400).
  p_hat = 248 / 400 = 0.62

2. Determine the confidence level (95%) and find the corresponding z-score. For a 95% confidence level, the z-score is 1.96.

3. Calculate the margin of error (ME) using the formula:
 [tex]ME = z-score \sqrt{\frac{(p_hat)(1-p_hat)}{n} }[/tex]
  [tex]ME = 1.96 \sqrt{\frac{0.062(1-0.62)}{400} }[/tex]
  ME = 0.048

4. Calculate the 95% confidence interval:
  Lower bound = p_hat - ME = 0.62 - 0.048 =0.572
  Upper bound = p_hat + ME = 0.62 + 0.048= 0.668

Based on the 95% confidence interval, we can estimate that the proportion of the entire voting population (p) that prefers Candidate A is between 0.572 and 0.668, expressed as decimals to three places.

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The circumference of the circle-shaped garden is 157 meters.

The gardener will need 157 meters of fencing to outline the garden.

We have,

The circumference of a circle is given by the formula C = πd, where d is the diameter.

Using this formula,

C = πd

C = 3.14 × 50

C = 157 meters

Therefore,

The circumference of the circle is 157 meters.

The gardener will need 157 meters of fencing to outline the garden.

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If the null hypothesis were true, the sample correlation would be expected to be near 0, and it is very unlikely to obtain a correlation as strong as -0.67.

a. The sample correlation between self-reported political orientation and support for the legalization of medical marijuana is r = -0.67. This negative correlation indicates that as political orientation becomes more conservative (higher score), support for the legalization of medical marijuana decreases (lower score). The correlation is moderate in size, which means that there is a meaningful relationship between these two variables.

b. The null hypothesis is that there is no correlation between self-reported political orientation and support for the legalization of medical marijuana in the population, symbolized as H0: ρ = 0. The alternative hypothesis is that there is a correlation in the population, symbolized as Ha: ρ ≠ 0.

c. The critical value for a two-tailed test with alpha level α = 0.05 and n = 30-2 = 28 degrees of freedom is ±2.048. The rejection regions are the two tails of the t-distribution with this critical value.

d. The appropriate t-test to answer this question is a two-tailed test of the population correlation coefficient using the formula: t = r√(n-2) / √(1-r^2). Plugging in the values from the sample, we get: t = -3.29.

e. We reject the null hypothesis because the calculated t-value (-3.29) falls outside the rejection region (±2.048). This means that the sample correlation is significantly different from 0, and we have evidence to support the alternative hypothesis that there is a correlation in the population. The p-value associated with the sample correlation is p < 0.01, which means that there is less than a 1% chance of obtaining a correlation as extreme as the one observed in the sample if the null hypothesis is true. This suggests strong evidence against the null hypothesis. If the null hypothesis were true, the sample correlation would be expected to be near 0, and it is very unlikely to obtain a correlation as strong as -0.67.

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Answer:

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

Area of square with side of 5 mm is:

Find total area of the figure:

Find the percent value of the ratio of areas of the square and full figure, which determines the probability we are looking for:

This is matching the choice C.

The value of x is equal to 17.

In Mathematics, the exterior angle theorem or postulate is a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the triangle BHY is equal to the measure of angle x (∠NYB);

m∠BHY + m∠HBY = m∠NYB

(2x + 7)° + (8x - 18)° = (4x + 91)°

10x - 11 = 4x + 91

10x - 4x = 91 + 11

6x = 102

x = 102/6

x = 17.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

75%

Step-by-step explanation:

We Know

Mandy collected 80 stamps last year.

Collected 140 stamps this year.
What was the percentage increase in her stamp collection?

We Take

(140 ÷ 80) x 100 = 175%

Then We Take

175 - 100 = 75%

So, the stamp collection increase by 75%

The radius of the region is 11.55 mile.

We have,

Population = 175,000

So, population density

= 175,000 / 1318

= 132.77

and, the radius using from the population density

Radius = √area / (22/7)

= √1318 x 7/22

= 11.55 mile

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We calculated x by multiplying the elementary matrices E1, E2, and E3:

x = E1E2E3 =

(1 0)   (1 5)    (-1/5 0)

(4 1) * (0 1) *  (0    1) =

(-4 1)

(0 -1)

A matrix is a set of numbers that are arranged in rows and columns. Rows and columns are not always present in all matrices since some of them do not follow the same rule.

To express x as a product of elementary matrices, we need to perform elementary row operations on the identity matrix until we obtain x.

Starting with the 2x2 identity matrix:

I = (1 0)

   (0 1)

We can perform the following row operations to obtain x:

1. Add 4 times the first row to the second row:

E1 = (1 0)

    (4 1)

I * E1 = (1 0)

        (4 1)

2. Add 5 times the second row to the first row:

E2 = (1 5)

    (0 1)

(I * E1) * E2 = (1 5)

               (0 1)

3. Multiply the first row by -1/5:

E3 = (-1/5 0)

(0    1)

((I * E1) * E2) * E3 = (-4 1)

(0 -1)

Therefore, we have expressed x as the product of the elementary matrices E1, E2, and E3:

x = E1E2E3 =

(1 0)   (1 5)    (-1/5 0)

(4 1) * (0 1) *  (0    1) =

(-4 1)

(0 -1)

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The 22nd term of the arithmetic sequence is 59.

We have,

2nd term of Arithmetic sequence= 9

and, 8th term = 24

So, a + d = 9....(1)

a+ 7d = 24...........(2)

Solving equation (1) and (2) we get

7d - d = 24 - 9

6d = 15

d = 5/2

and, a = 9 - 5/2 = 13/2

Now, the 22nd term of the sequence

= a + 21d

= 13/2 + 21(5/2)

= 13/2 + 105/2

= 118 /2

= 59

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The linear equations are parallel.

To find the relation between the lines we need to find the slopes.

To find the slope  of the lines we take the quotient between the difference in the y-values and the x-values.

For the points (1, -6) and (3,-2) the slope is:

a = (-2 + 6)/(3 - 1) = 4/2 = 2

For  the points (4,8) and (6, 12) the slope is:

a' = (12 - 8)/(6 - 4) = 4/2 = 2

The slopes are the same ones.

Now, the first line can be written as:

y = 2x + b

Replacing the values of the first point:

-6 = 2*1 + b

-6 - 2 = b

-8 = b

The line is y = 2x - 8

For the second line:

y = 2x + b'

We replace the point (4, 8) there:

8 = 2*4 + b'

8 = 8 + b'

0 = b'

This line is y = 2x

The lines have the same slope and different y-intercept, so the lines are parallel.

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The sum of all the three angles of a triangle is 180°.

x + x + 26.35° = 180°

2x = 180° - 26.35°

x = 76.825°.

Therefore, ∠P will be equal to 76.825°.

Answer:

∠P = 76.825°

Step-by-step explanation:

If angles P and Q are congruent, then triangle PQR is an isosceles triangle where ∠P and ∠Q are the base angles and ∠R is the apex angle.

The interior angles of a triangle sum to 180°. Therefore:

⇒ ∠P + ∠Q + ∠R = 180°

As ∠P = ∠Q and ∠R = 26.35°, then:

⇒ ∠P + ∠P + 26.35° = 180°

⇒ 2∠P + 26.35° = 180°

⇒ 2∠P + 26.35° - 26.35° = 180° - 26.35°

⇒ 2∠P = 153.65°

⇒ 2∠P ÷ 2 = 153.65° ÷ 2

⇒ ∠P = 76.825°

Therefore, the measure of angle P is 76.825°.

The map that shows the picnic table in the correct location is illustrated below.

Firstly, we need to understand the concept of scale on a map. Maps are often drawn to scale, which means that the distances between different points on the map represent a proportional distance in real life. For instance, if one inch on the map equals one mile in real life, then two inches on the map would represent two miles in real life.

To do this, we need to locate the campsite on the map and measure out 1.5 miles along Path A. Once we have done this, we can mark this location on the map as the location of the picnic table.

However, we need to make sure that we are using a map that is drawn to scale. Otherwise, we might not be able to accurately measure the distance and locate the picnic table correctly.

Therefore, we need to examine the different maps that we have and find one that is drawn to scale. Once we have found a suitable map, we can measure out the distance from the campsite to the location of the table along Path A, and mark it on the map.

Finally, we can compare the location we have marked on the map with the location of the table as described in the problem. If they match up, we have found the correct location of the table on the map.

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1.) [tex]y(y + 4) - y = 6[/tex] ✅Are Quadratic Functions.

2.)  [tex](3x + 2) + (6x - 1) = 0[/tex] ❌ Not a Quadratic Function.

3.) [tex]4b(b) = 0[/tex] ✅ Are Quadratic Functions.

4.) [tex]3a - 7 = 2 (7a - 3)[/tex] ❌ Not a Quadratic Function.

Answer:

A & C

Step-by-step explanation:

Got It right on edge.

The upper extreme of the given data set is 15.

Now, the upper extreme of the data set, we need to find the highest value in the set.

The given data set is;

⇒ 4, 4, 1, 3, 8, 9, 15, 13, 4, 1

Thus, find the upper extreme, we need to sort the data set in ascending order:

⇒ 1, 1, 3, 4, 4, 4, 8, 9, 13, 15

Thus, The highest value in the data set is 15, which is the upper extreme.

Therefore, the upper extreme of the given data set is 15.

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