3. every 15 minutes, remove the cover and check the temperatures of the samples using the three thermometers. wait 30 seconds before recording the thermometer reading. once the temperatures of the three samples are no more than a degree apart, record the temperatures.

Step-by-step explanation:

(4, 8)

they already give you your Y so if you find the middle between the bank and hospital and then find the number for the X theres your answer. That was confusing but im unsure how else to explain it ;-; sorry

When the y-coordinate of the second point is -2, the slope between the points (-2, 7) and (-5, r) will be equal to 3.

Let's begin by calculating the slope between the given points (-2, 7) and (-5, r) using the slope formula:

slope = (change in y-coordinates) / (change in x-coordinates)

The change in y-coordinates is given by: y₂ - y₁

The change in x-coordinates is given by: x₂ - x₁

Substituting the values of the points into the formula, we have:

slope = (r - 7) / (-5 - (-2))

To find the value of "r" that makes the slope equal to 3, we can set up the equation:

3 = (r - 7) / (-5 - (-2))

Now, let's solve this equation for "r":

Multiply both sides of the equation by (-5 - (-2)) to eliminate the denominator:

3 * (-5 - (-2)) = r - 7

Simplifying the left side of the equation:

3 * (-5 - (-2)) = 3 * (-5 + 2) = 3 * (-3) = -9

Now, we have:

-9 = r - 7

To isolate "r," we can add 7 to both sides of the equation:

-9 + 7 = r - 7 + 7

Simplifying:

-2 = r

Therefore, the value of "r" that makes the slope equal to 3 between the points (-2, 7) and (-5, r) is -2.

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50×100÷110=45.454545r6

The horizontal and vertical translations applied to ΔABC:

A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.

Given that,

\(\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right]\)   = ?

After using matrix operation it can be further solved as,

\(\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right]\)

Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

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Answer:

5x2+6x-6=0

Step-by-step explanation:

Standard form is ax2+bx+c=0

We add 6x to both sides and we get:

5x2+6x-6=0

The standard form of the equation of the ellipse which satisfy the given conditions with foci  (-4, 0). (4,0), and vertices  (-8, 0), (8,0) is given by x²+ 4y² = 64

foci of the ellipse = (-4, 0). (4,0),

and vertices of the ellipse = (-8, 0), (8,0)

To find the standard form of the equation of an ellipse,

Determine the center, major axis length, and minor axis length of the ellipse.

The foci (-4, 0) and (4, 0) and the vertices (-8, 0) and (8, 0),

Observe that the center of the ellipse is the midpoint between the foci and vertices, which is (0, 0).

The major axis length is the distance between the vertices,

which is 8 - (-8) = 16.

This corresponds to the length of the horizontal axis.

The minor axis length is the distance between the center and one of the foci, which is 4.

Now, use the standard form of the equation for an ellipse centered at the origin,

(x² / a²) + (y² / b²) = 1

Where 'a' represents the semi-major axis length

and 'b' represents the semi-minor axis length.

The semi-major axis length is 16/2 = 8 (half the major axis length),

and the semi-minor axis length is 4.

Plugging these values into the equation, we have,

⇒ (x² / 8²) + (y² / 4²) = 1

Simplifying,

⇒ (x² / 64) + (y² / 16) = 1

To convert it to the standard form of the equation of an ellipse,

Multiply both sides of the equation by 64.

64(x² / 64) + 64(y² / 16) = 64

Simplifying,

x² + 4y² = 64

Therefore, the standard form of the equation of the ellipse satisfying the given conditions is equal to x²+ 4y² = 64

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Answer:

Lana is saving at the greater rate.

Answer:

6.4 hours

or 6 hours and 24  minutes

Step-by-step explanation:

Going

Rate: 60

Time: 8

Distance: 480 (60 x8)

Coming

Rate: 75

Distance: 480 (the same as going)

time = \(\frac{480}{75}\) = 6.4

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Equation A

Equation B

Answer:

name a word problem where our number of the day is your solution

Correct Answer : C. Such data are not counts or measures of? anything, so it makes no sense to compute their average? (mean).

The average, also known as the mean, is a measure of central tendency in statistics. It is calculated by adding up a set of values and then dividing the sum by the total number of values in the set. The resulting number represents an estimate of the "typical" or "average" value in the set.

Clearly, the way in which data is collected, makes the collected data for variable "Favourite Food" strictly a categorical variable. It doesn't have any quantitative nature associated with it. So, it makes no sense to compute the mean.

Hence, option C is correct.

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B. The data given are categorical, not numerical or quantitative, which means the average (mean) cannot be found in the usual way. As such, it cannot be computed correctly with the given information.

The given calculation is wrong because the data given are categorical, not numerical or quantitative. This means that the average (mean) cannot be found in the usual way. To find the average (mean) in this case, the total number of respondents (698) must be divided by the number of categories (4) to get the average (mean) for each category. Then, each category can be assigned a numerical value (1 for Italian food, 2 for Mexican food, 3 for Chinese food, 4 for anything else). The numerical values for each category can then be multiplied by the number of respondents who chose that category and added together. Finally, the sum can be divided by the total number of respondents (698) to get the average (mean).

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Step-by-step explanation:

The two angles added together = a right angle = 90 degrees

so  8m+7    + 5m+5   = 90

      13m  + 12 = 90

     13m = 78

      m = 78/13 = 6

Answer:

o

Step-by-step explanation:

Answer:

5 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1 )^2 }\)

with (x₁, y₁ ) = (6, 4) and (x₂, y₂ ) = (3, 8)

d = \(\sqrt{(3-6)^2+(8-4)^2}\)

   = \(\sqrt{(-3)^2+4^2}\)

   = \(\sqrt{9+16}\)

    = \(\sqrt{25}\)

    = 5

Answer:

5

Step-by-step explanation:

Answer:

4400

Step-by-step explanation:

Answer:

One solution. x=1

Step-by-step explanation:

Answer:

The equation has 1 solution, x = 1

The statement "the standard deviation is equal to the square of the variance" is False.

In statistics, both the standard deviation and the variance are measures of variability or dispersion within a dataset.

However, they are distinct measures and not equal to each other.

The variance (σ²) is the average of the squared deviations from the mean.

It is calculated by summing the squared differences between each data point and the mean, and then dividing by the total number of data points. The variance is expressed in squared units of the original data.

On the other hand, the standard deviation (σ) is the square root of the variance.

It represents the average amount of deviation or dispersion of data points from the mean.

By taking the square root of the variance, the standard deviation is expressed in the same units as the original data, making it more interpretable and easier to compare across different datasets.

In summary, the standard deviation is not equal to the square of the variance. Rather, it is the square root of the variance.

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Answer:

x=-17

Step-by-step explanation:

Answer:

\(3x - 17 = 4x \\ \\ 3x - 4x = 17 \\ \\ x = - 17\)

Answer: Yes you can use the HL theorem

Explanation:

HL = hypotenuse leg

The tickmarks tell us about the congruent hypotenuse sides. This takes care of the "H" from "HL".

The "L" portion is because BC = BC (reflexive property) which are the congruent legs.

So we have enough info to use the HL theorem to prove the triangles are congruent.

Note: The HL theorem only works for right triangles.

Answer:

7723

Step-by-step explanation:

Trust me I'm just as confused as you are.

Using proportions, it is found that with an income of $57,890, you need to pay $12,735.8 in taxes.

A proportion is a fraction of a total amount.

In this problem, for incomes from $38,701 up to $82,500, you need to pay 22% in taxes. An income of $57,890 is in this range, hence the amount paid is given by:

A = 0.22 x 57890 = $12,735.8.

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Answer:

37.5 cm^2

Step-by-step explanation:

2.5 * 3.5 = 6.25

6.25 x 6 is 37.5

To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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Answer:

Step-by-step explanation:

\(x^2 + 4x + 4 = 12\\\\x^2+2\cdot x\cdot2+2^2=12\\\\(x+2)^2=12\\\\x+2=-\sqrt{12}\quad\vee\quad x+2=\sqrt{12}\\\\x=-2\sqrt{3}-2\quad\vee\quad x=2\sqrt3-2\)

The area bounded by the intersection of the curves are as follows to find the area bounded by the intersection of the curves y = 1 and y = x², we need to find the points of intersection and calculate the area between them.

Setting the equations equal to each other, we have:

1 = x²

Solving for x, we find:

x = ±1

So the curves intersect at the points (-1, 1) and (1, 1).

2. To find the area between the curves, we integrate the difference between the curves over the interval between the x-values of intersection points:

Area = ∫[from -1 to 1] (x² - 1) dx

Integrating the expression, we get:

Area = [x³/3 - x] [from -1 to 1]

= [(1/3 - 1) - (-1/3 + 1)]

= [(1/3 - 3/3) - (-1/3 + 3/3)]

= [(-2/3) - (2/3)]

= -4/3

Therefore, the area bounded by the intersection of the curves y = 1 and y = x² is -4/3 square units.

To determine the arc length of the curve y = 2√(3) + 1 for 0 ≤ x ≤ 1, we need to evaluate the integral of the square root of the sum of the squares of the derivatives of x and y with respect to x over the given interval.

The derivative of y = 2√(3) + 1 with respect to x is 0 since y is a constant.

The arc length integral can be written as:

Arc Length = ∫[from 0 to 1] sqrt(1 + (dy/dx)²) dx

Since (dy/dx)² = 0, the integral simplifies to:

Arc Length = ∫[from 0 to 1] sqrt(1 + 0) dx

= ∫[from 0 to 1] sqrt(1) dx

= ∫[from 0 to 1] dx

= [x] [from 0 to 1]

= 1 - 0

= 1

Therefore, the arc length of the curve y = 2√(3) + 1 for 0 ≤ x ≤ 1 is 1 unit.

3. To find the volume of the solid of revolution that results from revolving the region under the curve y = √(x + 4) for 0 ≤ x ≤ 2 about the x-axis, we can use the method of cylindrical shells.

The volume can be calculated using the formula:

Volume = ∫[from 0 to 2] 2πx √(x + 4) dx

Integrating the expression, we get:

Volume = 2π ∫[from 0 to 2] x √(x + 4) dx

This integral can be evaluated using techniques such as substitution or integration by parts. Once the integration is performed, the result will give us the volume of the solid of revolution.

Please note that the calculation of this integral is more involved, and the exact value will depend on the specific method used for integration.

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There are an endless number of solutions to a system of m n linear homogeneous equations with m n fewer equations than unknowns. As a result, such a system always has both the zero solution and the nonzero solution.

What is  infinite solution?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".

What is an infinite number?

There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.

                   The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.

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Answer:

2x^2 + 2x - 83 = 0

Step-by-step explanation:

Consecutive integers differ by 1

Let the first number be x

The next will be (x+1)

The sum of the squares of these two numbers is 85

so we have;

x^2 + (x + 1)^2 =85

= x^2 + x^2 + 2x + 2 = 85

2x^2 + 2x + 2-85 = 0

2x^2 + 2x - 83 = 0

The output of the LTI system with frequency response function \(h(w) = 1/(jw^3)\), given an input\(x(t)\), is:

\(y(t)\)= inverse Fourier transform of \([1/(jw^3) X(w)]\)

To compute the output of an LTI system with frequency response function \(h(w) = 1/(jw^3)\), given an input x(t), we can use the Fourier transform:

\(H(w)\) = Fourier transform of \(h(t)\)

\(X(w)\) = Fourier transform of \(x(t)\)

\(Y(w) = H(w) X(w)\)

\(Y(w)\) is the Fourier transform of the output \(y(t)\).

Using the given frequency response function, we have:

\(H(w) = 1/(jw^3)\)

Taking the Fourier transform of the input \(x(t)\), we have:

\(X(w)\) = Fourier transform of \(x(t)\)

And multiplying \(H(w)\) and\(X(w)\), we get:

\(Y(w) = H(w) X(w) = 1/(jw^3) X(w)\)

Taking the inverse Fourier transform of \(Y(w)\), we get the output \(y(t)\):

\(y(t)\) = inverse Fourier transform of \(Y(w)\)

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Answer:

The answer is 639.

Step-by-step explanation:

42.6 × 15

639

Answer: 639

Step-by-step explanation:

42.6 x 15 =639

The probability that the dictionary is selected is 0.417, 3 novels and 2 books of poems are selected is 0.707. The probability that 4 novels are selected is 0.354.

The probability that the dictionary is selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select the dictionary and 4 other books.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select the dictionary and 4 other books is:

C(1,1) * C(11,4) = 11! / (4! * 7!) = 330

Therefore, the probability that the dictionary is selected is:

P(dictionary) = 330/792 = 0.417

The probability that 3 novels and 2 books of poems are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 3 novels and 2 books of poems.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select 3 novels and 2 books of poems is:

C(8,3) * C(3,2) = (8! / (3! * 5!)) * (3! / (2! * 1!)) = 560

Therefore, the probability that 3 novels and 2 books of poems are selected is:

P(3 novels, 2 books of poems) = 560/792 = 0.707

The probability that 4 novels are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 4 novels and 1 other book.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select 4 novels and 1 other book is:

C(8,4) * C(4,1) = (8! / (4! * 4!)) * (4! / (1! * 3!)) = 280

Therefore, the probability that 4 novels are selected is:

P(4 novels) = 280/792 = 0.354

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_____ The given question is incomplete, the complete question is given below:

If 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that a. the dictionary is selected? b. 3 novels and 2 books of poems are selected? c. 4 novels are selected?