The equation N(t)=5501+49e−0.7t models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N(t) approach? Interpret your answer. How many people started the rumor? N(t) approaches . N(t) is limited by the number of poeple who started the rumor. N(t) is limited by the carrying capacity of the town. N(t) is limited by the number of days it takes for the entire population to hear the rumor. N(t) is limited by the rate at which the rumor spreads. N(t) is not limited by any value and increases without bound.

Answer:

(-3, -5)

Step-by-step explanation:

When reflected over the x-axis, the x remains the same, and the y change to their opposite sign.

So, the answer is (-3, -5)

The two possible locations for the fourth vertex of the parallelogram are p and q.

The fourth vertex of a parallelogram can be obtained by adding the vector difference between two of its vertices to the third vertex. In this case, the vector difference between two vertices can be found by subtracting one vertex from the other, i.e. p-o and q-o. So, the fourth vertex can be found by adding either of these vectors to vertex o, i.e. r = p - o + o = p or r = q - o + o = q.

Therefore, the two possible locations for the fourth vertex of the parallelogram are p and q.

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Classifying polynomials refers to categorizing polynomials based on the degree of the polynomial and the number of terms in the polynomial.

The degree of a polynomial is the highest exponent in the polynomial. Polynomials can be classified into several types, including constant polynomials (degree 0), linear polynomials (degree 1), quadratic polynomials (degree 2), and so on. Adding and subtracting polynomials is the process of combining two or more polynomials by combining like terms. Like terms are terms with the same variable and exponent. To add or subtract polynomials, simply line up the terms with the same variable and exponent and add or subtract the coefficients. The result will be a new polynomial with the combined terms.

For example, to add the polynomials [tex]2x^2 + 3x + 4[/tex] and [tex]-x^2 + 5x - 6[/tex], we line up the terms with the same variable and exponent and add the coefficients:

[tex](2x^2 + 3x + 4) + (-x^2 + 5x - 6) = (2x^2 - x^2) + (3x + 5x) + (4 - 6) \\[/tex]

                                                   [tex]= x^2 + 8x - 2.[/tex]

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Answer:

Step-by-step explanation:

10x+y=9(x+y)

10y+x=10x+y-63

now put x alone and solve for x then y and add the values of x and y and you will get your answer

The probability of randomly selecting a pop CD is 15/74.

Probability is a measure of the likelihood of a certain event occurring, expressed as a number between 0 and 1.

An event with a probability of 1 is considered certain to occur, while an event with a probability of 0 is considered impossible. Events with probabilities between 0 and 1 are considered uncertain, with higher probabilities indicating greater likelihood of occurrence.

Probability is a mathematical concept that represents the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur. The calculation of probability involves using rules of probability theory and statistical analysis to determine the chance of a specific outcome or set of outcomes.

There are various methods for calculating probability, including classical probability, empirical probability, and subjective probability.

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Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.

What is arithmetic sequence ?

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

The sequence {12, 5, -2, -9, -16 ... } can be defined by the following items:

The first term: 12

The common difference: -7

The pattern of adding the common difference to find the next term.

Therefore, all the items that define the sequence are:

The first term: 12

The common difference: -7

This sequence is an arithmetic sequence.

Arithmetic sequence {12, 5, -2, -9, ...} defined by first term 12 and common difference -7.

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Since C is any arbitrary constant,  [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.

The equation given to us is:

[tex](3 + x^{10})\frac{dy}{dx} = \frac{x^{9}}{y}[/tex]

We can re-write the above equation:

[tex]y dy = \frac{x^9}{3 + x^{10}} dx[/tex]

This is separation of variables.

A separable differential equation is any equation that can be written in the form y′=f(x)g(y). The method of separation of variables is used to find the general solution to a separable differential equation.

Now, if we differentiate the denominator,

[tex]\frac{d}{dx} (3 + x^{10} ) = 10x^9[/tex]

Integrating both sides,

[tex]\frac{y^2}{2} = \frac{1}{10} ln (3 + x^{10})[/tex] + C

⇒ [tex]y^{2} = \frac{1}{5} ln (3 + x^{10})[/tex] + 2C

Since C is any arbitrary constant,  [tex]y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C[/tex] is the final solution of the differential equation.

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The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

1. Place the graduated pipet on a flat surface and make sure it is level

2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume

3. Make sure the liquid is not touching the etched line above it

4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines

The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

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The Probability that only one of John's pot crack while being fired is 0.06.

The probability that only one of John's pots cracks while being fired can be calculated using the formula for the binomial distribution:

P(X = 1) = C(2, 1) * (0.03)^1 * (1 - 0.03)^(2 - 1)

= 2 * 0.03 * 0.97

= 0.0582

Where C(2, 1) is the number of combinations of 2 items taken 1 at a time, and (0.03)^1 and (1 - 0.03)^(2 - 1) are the probabilities of the first pot cracking and the second pot not cracking, respectively.

So, the probability that only one of John's pots cracks while being fired is approximately 0.06.

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The value of the sample variance rounded to one decimal place is 76.0.

What is the Mean?

The mean is a measure of the central tendency of a set of data, calculated as the sum of the values divided by the number of values in the set.

The sample variance of a set of data is a measure of the spread or dispersion of the data around the mean. To calculate the sample variance, you can follow these steps:

Calculate the mean of the data: First, find the sum of all the data points and divide by the number of data points (n).

For the given data, the mean is: (-11 + -5 + -5 + -11 + 13 + -11 + -5) / 7 = -7

Subtract the mean from each data point: Next, subtract the mean from each data point to get the deviations from the mean.

For the given data, the deviations are: (-11 - -7) = -4, (-5 - -7) = 2, (-5 - -7) = 2, (-11 - -7) = -4, (13 - -7) = 20, (-11 - -7) = -4, (-5 - -7) = 2

Square the deviations: Square each deviation to get rid of negative values.

For the given data, the squared deviations are: (-4)^2 = 16, (2)^2 = 4, (2)^2 = 4, (-4)^2 = 16, (20)^2 = 400, (-4)^2 = 16, (2)^2 = 4

Sum the squared deviations: Sum all the squared deviations.

For the given data, the sum of the squared deviations is: 16 + 4 + 4 + 16 + 400 + 16 + 4 = 456

Divide the sum by n - 1: Finally, divide the sum of the squared deviations by the number of data points minus 1 (n - 1). This gives us the sample variance.

For the given data, the sample variance is: 456 / (7 - 1) = 456 / 6 = 76

Hence, the value of the sample variance rounded to one decimal place is 76.0.

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The number of boxes with three of them are 44.

Two or more expressions with an Equal sign is called as Equation.

Given that Fells had 9 boxes.

Dylan had 2 times minus 1 boxes than Fells.

2(9)-1 which is 18-1= 17 boxes.

Scarlett had 18 boxes but fewer than Dylan

The total number of boxes are 9+17+18

44 boxes

Hence, the number of boxes with three of them are 44.

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The number of batches of soup that Fabian can make is given as follows:

3 batches.

The number of batches of soup is obtained applying the proportions in the context of the problem.

He has 10 pounds, and sets aside 2.8 pounds of tomatoes to make spaghetti sauce, hence the amount remaining for soup is given as follows:

10 - 2.8 = 7.2 pounds.

He needs 2 and 2/5 = 2 + 0.4 = 2.4 pounds for each batch, hence the number of batches is obtained as follows:

7.2/2.4 = 3.

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Answer: 3

Step-by-step explanation:

Zero is the magnitude of the electric field inside the conducting shell, at a radial distance r where a < r < b.

Each point in space has an electric field associated with it when there is charge existing in any form. E, often known as electric field strength, electric field intensity, or just the electric field, is a mathematical constant that expresses the strength and direction of an electric field.

The electromagnetic region which surround electrically charged particles and acts to either attract or repel all those other positive ions in the field is known as an electric field (or E-field). A systems of charged particles' physical field is also referred to in this phrase.

By applying Gauss law, to the sphere of radius r with dotted lines:

∅(E) = ∫E. dA

∅(E) = E (4πr²) = Q/∈₀

E₁ = Q/4πr²∈₀

The electric field in a conductor is zero. a < r < b has an r value in the conductor.

E₂ = 0

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3/4 and 5 18 is fraction have a leat common denominator of 36.

3/4 and 5 18 is fraction have a leat common denominator of 36.

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To find f ( -4 ) - f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. Now that we have both values we can subtract them to get the answer of -67.

a.) f ( -4 ) = 3 ( -4 )2 - 4 ( -4 ) - 5 = -47  f ( 3 ) = 3 ( 3 )2 - 4 ( 3 ) - 5 = 20  f ( -4 ) f ( 3 ) = -47 ( 20 ) = -940

b.) f ( -4 ) - f ( 3 ) = -47 - 20 = -67

a.) To find f ( -4 ) f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. This gives us -47. To evaluate f ( 3 ) we plug 3 into the function and simplify. This gives us 20. Now that we have both values we can multiply them together to get the answer of -940.

b.) To find f ( -4 ) - f ( 3 ) we need to first evaluate both functions. To evaluate f ( -4 ) we plug -4 into the function and simplify. This gives us -47. To evaluate f ( 3 ) we plug 3 into the function and simplify. This gives us 20. Now that we have both values we can subtract them to get the answer of -67.

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The probability for getting the different numbers when two dice are thrown is: 5/6.

The sample space formed by rolling two dice are: 6*6 = 36.

Total number of pairs having same number = (1,1), (2,2),(3,3),(4,4),(5,5),(6,6) = 6 samples.

Thus,

Number of outcomes having different numbers:

36 - 6 = 30

Probability (different numbers) = total number of different number / total outcomes.

Probability (different numbers) = 30 / 36

Probability (different numbers) = 5/6

Thus, the probability for getting the different numbers when two dice are thrown is: 5/6.

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The limit does not exist as x approaches 8 for (√(12−x) − 2)/ (√(24−x) − 4).

Therefore the answer is dne.

The square root of 12 - x approaches 2 as x approaches 8 and the square root of 24 - x approaches 4 as x approaches 8.

The limit fails to exist because both the numerator and the denominator approach 0 as x approaches 8, but the ratio of the two approaches positive infinity. This shows that the limit is undefined or "dne".

As both the numerator and denominator approach 0, the fraction they form can approach any real number or it can oscillate between two values, leading to an undefined limit. In such cases, the limit fails to exist.

--The question is not readable, answering to the question below--

"evaluate the limit, if it exists. (if an answer does not exist, enter dne.)

lim x → 8 (√(12−x) − 2)/ (√(24−x) − 4)"

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Substance Gallons         % Fruit Juice

Drink A              x                         20%

Drink B              y                          5%

Total         x + y = 30                  10%

To find the number of gallons of Drink A and Drink B that should be used, we can write two equations based on the percentage of fruit juice.

20% * x = 10% * (x + y)

5% * y = 10% * (x + y)

Simplifying and solving for x and y:

x = 1.5 * y

10% * (x + y) = 10% * 30

y = 15

x = 1.5 * 15 = 22.5

So, we would use 22.5 gallons of Drink A and 15 gallons of Drink B to make a 30 gallon mixture that is 10% fruit juice.

In a case whereby Mrs. Carter's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil the amount of peanut butter she should use can be expressed as  2 cups of peanut butter.

The concept that will be used is simplification. Base on the provided information from the question,

(1/2 cup of oil )= (1 cup of peanut butter)

we can represent (1 cup of oil)  as  (x)

The if we perfor a Cross Multipliplication we have:

(1/2x) =( 1 × 1)

x = (1 × 2/1)

x = 2 cups of peanut butter.

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On solving the provided question, we can say that the equation foe the rectangle will be = 34 = 12 + 2W

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Perimeter of rectangle is = 2(L+W)

the equation foe the rectangle will be =

34 = 2(6.5 + W)

34 = 12 + 2W

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The proportionate equation for each problems are:

Let's discuss each problem we have:

1. Liv earns $9.50 for every 2 bracelets she sells.

y = 4.75x

because y = kx, then:

y = $9.50

x = 2

4.75 --> constant of proportionality

--> price per unit of bracelet sold

2. John ran 3 miles in 25.5 minutes

y = 8.5x

y = 25.5 minutes

x = 3 miles

8.5 --> constant of proportionality

--> minuntes per miles

--> times per distance

3. Lincoln bought 3 bottles of energy drink for $4.50

y = kx

y = $4.50

x = 3

$4.50 = k (3)

k = $1.50 --> price of a bottle of energy drink

4.  Total cost of 4 hours renting a cotton candy machine is $72.

y = kx

y = $72

x = 4 hours

$72 = k(4)

k = $18 --> price of renting per hour

5. 7 cups of water are used to make 4 loaves of French bread.

y = kx

y = 7

x = 4

7 = k(4)

k = 7/4

Proportionate equation: y = 7/4 x

(x = 6)

y = 7/4 (6)

y = 21/2 = 10.5 cups of water

6. 6 3/4 yards of fabrics are used to make 3 elf costumes

y = kx

y = 6 3/4

x = 3

6 3/4 = k (3)

27/4 = 3k

--------------- x 4

27 = 12k

k = 9/4

Proportionate equation: y = 9/4 x

(x = 7)

y = 9/4 (7)

y = 63/4

y = 15 3/4 yards of fabric

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Answer:

$5,250 ≤ m ≤ $6,125

Step-by-step explanation:

A compound inequality is a mathematical statement that combines two inequality statements using "and" or "or". In this case, the compound inequality represents the range of possible monthly salary for an entry-level mechanical engineer in Texas.

The average salary for this position ranges from $63,000 to $73,500 per year. To find the monthly salary, we need to divide these amounts by 12 months, which gives us the minimum and maximum monthly salary:

$63,000/12 = $5,250

$73,500/12 = $6,125

Therefore, the compound inequality is:

$5,250 ≤ m ≤ $6,125

This means that the monthly salary of an entry-level mechanical engineer in Texas could be anywhere between $5,250 and $6,125.

The domain and range of the ordered pair  {(-13, 9), (-7, -5), (5, 14). (11, -10)) is as follows:

domain = [-13, -7, 5, and 11]

range = {9, -5, 14 and -10}

The domain of a function is independent variable of a function. The domain is the input value of the function. The domain lies on the x axis of the function.

Therefore, the domain of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) is [-13, -7, 5, and 11]

The range is the dependent value of the function. The range is also called the output value of the function. The range lies on the y-axis of the function.

Therefore, the range of the ordered pair {(-13, 9), (-7, -5), (5, 14). (11, -10)) are {9, -5, 14 and -10}

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Answer:

False. The two sides evaluate to different numbers.

Step-by-step explanation:

Let's evaluate each side:

4 × (3 + 5) - 10 = 4 × 8 - 10 = 32 - 10 = 22

4 × 3 + 5 - 10 = 12 + 5 - 10 = 17 - 10 = 7

Answer:

Step-by-step explanation:

-4

Work Shown:

[tex]a_1 = -1 = \text{ first term} \\\\d = 0.5 = \text{ common difference} \\\\a_n = a_1 + d(n-1)\\\\a_n = -1 + 0.5(n-1)\\\\a_6 = -1 + 0.5(6-1)\\\\a_6 = -1 + 0.5(5)\\\\a_6 = -1 + 2.5\\\\a_6 = 1.5\\\\[/tex]

The probability that the battery will last for 52 months is approximately 0.928, or 92.8%.

To calculate the probability that a battery will last for 52 months, we need to find the z-score of 52 months, using the formula:

z = (x - μ) / σ

Plugging in the values, we get:

z = (52 - 42.5) / 6.5 = 1.384615

Next, we can use a z-table to find the probability that a battery will last more than 52 months.

In this case, the z-score is positive, so we look up the area to the right of 1.384615 in the z-table. The area to the right of 1.384615 is approximately 0.928.

Therefore, the probability that a battery will last for 52 months or more is approximately 0.928, or 92.8%.

So the answer to the question is: A) 92.8%

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The direction of A for the given indices of the cubic unit cell is:

A = [3 3 -1].

A notation used to pinpoint crystal planes is called a Miller index.

For the direction of A:

Direction of A = [(1 - 0) ,  (1 - 0), (1/3 - 2/3)]

                       = [ 1  1  -1/3]

Multiply each by 3.

                       = [3  3   -1]

Thus, the  direction of A for the given indices of the cubic unit cell is:

A = [3 3 -1].

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The complete question is-

Determine the indices for A, the directions shown in the following cubic unit cell.

The diagram is attached:

Answer:

Step-by-step explanation:

The probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

The probability that the digit 7 doesn't appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely is given by the probability that all 100 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 8, 9}. There are 10 choices for each digit, so there are 10^100 possible sequences of 100 digits. The number of sequences that don't contain the digit 7 is 9^100. Therefore, the probability that the digit 7 doesn't appear among 100 digits is: P(7 doesn't appear) = (9^100) / (10^100) = 9 / 10

Therefore, the probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

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Answer:

The point you would plot would be at -1/2

Explanation:

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