Question The graph shows a predicted population as a function of time. Which statement is true? Responses There is no limit to the population, but there is a limit to the number of months. There is no limit to the population, but there is a limit to the number of months. As the number of years increases without bound, the population decreases without bound. As the number of years increases without bound, the population decreases without bound. As the number of years decreases, the population increases without bound. As the number of years decreases, the population increases without bound. As the number of years increases without bound, the population increases without bound.

Answer: 120

Step-by-step explanation:V= 8x5x3 =120 ^3

Answer:

3x + 5x = 96

8x = 96, so x = 12

There are currently 3(12) = 36 pens and 5(12) = 60 pencils in the box, so 60 - 36 = 24 more pens should be put in the box.

Answer:166.2 feet^2

Step-by-step explanation:

By assuming that Pete's yard is a rectangle, we can get the perimeter by using an equation that looks like this:

perimeter = l+l+w+w

Where l = length, and w = width.

This is because you are adding the measures of every side together, which is the definition of the value of a perimeter.

Furthermore, to get the area of the figure, you would need to multiply 52.7 by 30.4, which would be 1602.08 feet^2

The winner using the pairwise comparison method is found to be Ontario. The correct answer is option c.

11 members of the town board must decide where to build a new post office.

Using the pairwise comparison method, we compare each choice against the other two.

For Lehigh Road (L) vs. Erie Road (E): L receives 5 votes and E receives 2 votes. Therefore, L wins this comparison.

For Lehigh Road (L) vs. Ontario Road (O): L receives 2 votes and O receives 4 votes. Therefore, O wins this comparison.

For Erie Road (E) vs. Ontario Road (O): E receives 2 votes and O receives 4 votes. Therefore, O wins this comparison.

Based on these pairwise comparisons, Ontario Road (O) wins with a total of 8 votes, followed by Lehigh Road (L) with a total of 7 votes, and Erie Road (E) with a total of 4 votes.

Therefore, the correct answer is the option c. Ontario

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a. The correlation matrix p =  [tex]\left[\begin{array}{ccc}1&1/3&2/5\\1/3&1&-3/5\\2/5&-3/5&1\end{array}\right][/tex]. b. The correlation between X1, and i/2X2 + 1/2X3 is 0.3.

a. The correlation matrix p can be calculated by dividing the covariance matrix by the product of the standard deviations of the variables:

p = [tex]\left[\begin{array}{ccc}1&1/3&2/5\\1/3&1&-3/5\\2/5&-3/5&1\end{array}\right][/tex]

b. To compute the correlation between X1 and i/2X2 + 1/2X3, we first need to calculate the standard deviations of the variables:

σ1 = sqrt(4) = 2

σ2 = sqrt(9) = 3

σ3 = sqrt(25) = 5

Then, we can calculate the covariance between X1 and i/2X2 + 1/2X3:

cov(X1, i/2X2 + 1/2X3) = cov(X1, i/2X2) + cov(X1, 1/2X3)

= i/2 * cov(X1, X2) + 1/2 * cov(X1, X3)

= i/2 * 1 + 1/2 * 2

= 1.5

Finally, we can compute the correlation using the formula:

corr(X1, i/2X2 + 1/2X3) = cov(X1, i/2X2 + 1/2X3) / (σ1 * σ2/2 + σ3/2)

= 1.5 / (2 * 3/2 + 5/2)

= 0.3

Therefore, the correlation between X1 and i/2X2 + 1/2X3 is 0.3.

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Answer:

The answer is 10 and -10

You get this answer because in the middle in a number line is 0 and if it 10 units from 0 then the other side of 0 will be -10 (negative ten) units from 0

Answer:

I believe (3, 5) and (10, 1) is the answer

Step-by-step explanation:

Answer:

-883 - 1

Step-by-step explanation:

A call that lasts for a length of 4 minutes would cost the same at either hotel.

For Hotel A: Cost = 2(4) + 5 = 13

For Hotel B: Cost = 4(4) - 3 = 13 minutes

We can determine the length of phone call that would cost the same at either hotel by the following equations.

Given:

Hotel A, cost of the call:

Cost for Hotel A = 2x + 5

For Hotel B, the cost of the call:

Cost for Hotel B = 4x - 3

For the length of the call that would cost the same at either hotel, we shall set these two equations equal to each other and solve for x:

2x + 5 = 4x - 3

Subtracting 2x from both sides, we get:

5 = 2x - 3

Adding 3 to both sides, we get:

8 = 2x

Dividing both sides by 2, we get:

x = 4

So, a call that lasts 4 minutes would cost the same at either hotel.

We can verify this, let's plug x = 4 into both equations:

For Hotel A: Cost = 2(4) + 5 = 13

For Hotel B: Cost = 4(4) - 3 = 13

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The coordinates of the point (-7,-3) after a 90 degree clockwise rotation about the origin are (-3,-7).

To rotate a point 90 degrees clockwise about the origin, we need to swap its x and y coordinates and negate the new x coordinate.

So, starting with point (-7,-3):

Swap the x and y coordinates to get (3,-7)

Negate the new x coordinate to get (-3,-7)

Therefore, the coordinates of the point (-7,-3) after a 90 degree clockwise rotation about the origin are (-3,-7).

In mathematics, coordinates are used to specify the position of a point or an object in a particular space. The number of coordinates needed depends on the dimension of the space in which the point or object exists.

In two-dimensional space (also called the Cartesian plane), a point is located by two coordinates, usually denoted as (x, y), where x represents the horizontal distance from a fixed reference point called the origin, and y represents the vertical distance from the origin.

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The complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).

What is complex number?

A complex number is obtained by adding real and imaginary numbers. Complex numbers have the formula a + ib and are usually symbolized by the symbol z. Here the numbers a and real are both. The value "a" is known as the real component and is denoted Re(z), while "b" is known as the imaginary part and is denoted Im(z). Also known as imaginary number, ib. Hero of Alexandria, a Greek mathematician, first used the idea of complex numbers in the first century when he tried to calculate the square root of a negative integer.

a. A complex number is a number that consists of a real part and an imaginary part, where the imaginary part is the real number multiplied by the imaginary unit "i", defined as the square root of -1. The modulus of a complex number is the distance between the starting point and the point representing the complex number on the complex plane. This can be calculated using the Pythagorean theorem. For example, the real part of the complex number z = 3 + 4i is 3 and the imaginary part is 4, and its modulus is √(3²+4²)=5.

b. Let z = a + bi be a complex number, where a and b are real numbers. The modulus of z is defined as |z| = √(a² + b²). Therefore, for the complex number z = 1 + 2i, the modulus is |z| = √(1² + 2²) = √5.

c. To write the complex number 2 = ((2+ m) + 3i) in polar form, we need to find the modulus and argument of the complex number. The modulus is |2 + ((2+m) + 3i)| = |4 + mi + 3i| = √(4² + (m+3)²) = √(m² + 6m + 25). The argument is given by tan⁻¹(Im/Re) = tan⁻¹(3/(2+m)), which gives us the angle that the complex number makes with the positive real axis. Therefore, the complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).

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The choice that matches the graph of the function as is defined to us is:  Graph A.

We are given a function f(x) as:

    f(x)=   2x    if x < 3

 and        4     if  x ≥ 3

This means that in the region (-∞,3) the graph of a function is a straight line that passes through the origin and has a open circle at x=3.

Also, in the region [3,∞) the graph is a straight horizontal line i.e. y=4.

Hence, the graph of this function is Graph A.

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On a piece of paper, graph f(x)={2x if x <3

{4 if x >3. Then determine which answer choice matches the graph you drew

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 11\%\to \frac{11}{100}\dotfill &0.11\\ t=years\dotfill &8 \end{cases} \\\\\\ A = 800e^{0.11\cdot 8}\implies A=800e^{0.88} \implies A \approx 1928.72[/tex]

According to the information presented on the box plot:

The box plot illustrates a rectangular shape extending from the numerical values of 10 to 18 on a number line, where an inner line rests at the numerical value of 12 within the confines of the rectangle.

The median functions as the numeric value that effectively splits data in half, equally distributing percentages of 50% below and above it while defining its centrality.

In this case, the statement "A line in the box is at 12" defines the median.

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If the  teacher explained that you can estimate how far away a lightning strike is by counting the number of seconds.

A linear function is used to calculate how far away lightning is depending on how long it takes to hear thunder.

The function is represented by the equation:

Distance = Time × Speed

Where:

Distance is measured in miles

Speed is measured in miles per second =  1 mile per 5 seconds

Time is measured in seconds as the duration of the thunderclap.

The equation is

Distance  = (1/5) x time

Therefore the equation for the function is g(x) = 1/5x.

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D. four. we can see that there are exactly four different groups of four that can be formed while adhering to the given conditions.

To answer this question, we need to find the number of different groups of four that can be formed while adhering to the given conditions for attending the retirement dinner.

1. Either J or K must be selected, but not both.
2. Either N or P must be selected, but not both.
3. N cannot be selected unless L is selected.
4. Q cannot be selected unless K is selected.

Let's find the different acceptable groups step by step:

Case 1: J is selected, P is selected
- J, P, L, M (L must be selected since N is not selected)

Case 2: J is selected, N is selected
- J, N, L, M (L must be selected because of condition 3)

Case 3: K is selected, P is selected
- K, P, L, M (Q cannot be selected because P is selected)

Case 4: K is selected, N is selected
- K, N, L, Q (L must be selected because of condition 3, and Q can be selected because of condition 4)

From the four cases listed, we can see that there are exactly four different groups of four that can be formed while adhering to the given conditions.

Your answer: D. four

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Answer:

THESE NUTS

Step-by-step explanation:

Answer:5

explanation:

you are doing great finding the slopes:

The differential   [tex]dy=2[/tex] when [tex]x = 4[/tex]  and [tex]dx = 0. 2.[/tex]

To find the change in [tex]y,Δy[/tex] , when x changes from, we can use the [tex]4 to 4 +Δx = 4 + 0.2 = 4.2[/tex] formula:

[tex]Δy = y(x + Δx) - y(x)[/tex]

where[tex]y(x) = 5x^2.[/tex]

So, plugging in[tex]x = 4[/tex] and[tex]x + Δx = 4.2[/tex] , we get:

[tex]Δy = y(4.2) - y(4)[/tex]

[tex]= 5(4.2)^2 - 5(4)^2[/tex]

[tex]= 44.2[/tex]

Therefore, the change in y is [tex]44.2[/tex] when x changes from [tex]4 to 4.2.[/tex]

To find the differential dy when [tex]x = 4[/tex] and [tex]dx = 0.2,[/tex]  we can use the formula:

[tex]dy = f'(x) × dx[/tex]

where the derivative of y with respect to x, which is:

[tex]f'(x) = 10x[/tex]

Plugging in [tex]x = 4[/tex]   we get:

[tex]= 2[/tex]

Therefore, the differential [tex]dy = 2[/tex] when [tex]x = 4[/tex] and [tex]dx = 0.2.[/tex]

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Rose sold 53.6 pretzels.

P x ? + W = 135

2.50 x 53.6 + 1.00 = 135

The number of different arrangements that can be formed is 7920

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

Pictures = 11

Arranged pictures = 6

These can be represented as

n = 11 and r = 6

The number of different arrangements that can be formed is

Number = nPr

So, we have

Number = 11P4

Evaluate

Number = 7920

Hence, the arrangements are 7920

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The first positive root of the function f(x) = x² - 3 is located between x = 1 and x = 2.

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b] and takes on values f(a) and f(b) with opposite signs, then there exists at least one root (zero) of the function between a and b.

In this case, we have f(x) = x² - 3. To find the first positive root of the function, we need to look for a positive value of x where f(x) = 0.

We can start by evaluating f(0) and f(2), which are the values of the function at the endpoints of the interval [0, 2]:

f(0) = 0² - 3 = -3

f(2) = 2² - 3 = 1

Since f(0) is negative and f(2) is positive, by the Intermediate Value Theorem, there must be at least one root of the function between x = 0 and x = 2.

To further narrow down the location of the root, we can evaluate f(1), which is the midpoint of the interval [0, 2]:

f(1) = 1² - 3 = -2

Since f(1) is negative, we know that the root is between x = 1 and x = 2.

To summarize, the first positive root of the function f(x) = x² - 3 is located between x = 1 and x = 2.

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To find a polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i, we know that the complex conjugate of 2-i, which is 2+i, must also be a zero. This is because complex zeros of polynomials always come in conjugate pairs.

So, we can start by using the factored form of a polynomial:

f(x) = a(x - r1)(x - r2)(x - r3)...

where a is a constant and r1, r2, r3, etc. are the zeros of the polynomial. In this case, we have:

f(x) = a(x - 5)(x - (2-i))(x - (2+i))

Multiplying out the factors, we get:

f(x) = a(x - 5)((x - 2) - i)((x - 2) + i)
f(x) = a(x - 5)((x - 2)^2 - i^2)
f(x) = a(x - 5)((x - 2)^2 + 1)

To make sure that f(x) only has real coefficients, we need to get rid of the complex i term. We can do this by multiplying out the squared term and using the fact that i^2 = -1:

f(x) = a(x - 5)((x^2 - 4x + 4) + 1)
f(x) = a(x - 5)(x^2 - 4x + 5)

Now, we just need to find the value of a that makes the degree of f(x) as small as possible. We know that the degree of a polynomial is determined by the highest power of x that appears, so we need to expand the expression and simplify to find the degree:

f(x) = a(x^3 - 9x^2 + 24x - 25)
Degree of f(x) = 3

Since we want the least degree possible, we want the coefficient of the x^3 term to be 1. So, we can choose a = 1:

f(x) = (x - 5)(x^2 - 4x + 5)
Degree of f(x) = 3

Therefore, the polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i is:

f(x) = (x - 5)(x^2 - 4x + 5)
To find a polynomial function f(x) of least degree with real coefficients and zeros of 5 and 2-i, we need to remember that if a polynomial has real coefficients and has a complex zero (in this case, 2-i), its conjugate (2+i) is also a zero.

Step 1: Identify the zeros
Zeros are: 5, 2-i, and 2+i (including the conjugate)

Step 2: Create factors from zeros
Factors are: (x-5), (x-(2-i)), and (x-(2+i))

Step 3: Simplify the factors
Simplified factors are: (x-5), (x-2+i), and (x-2-i)

Step 4: Multiply the factors together
f(x) = (x-5) * (x-2+i) * (x-2-i)

Step 5: Expand the polynomial
f(x) = (x-5) * [(x-2)^2 - (i)^2] (by using (a+b)(a-b) = a^2 - b^2 formula)
f(x) = (x-5) * [(x-2)^2 - (-1)] (since i^2 = -1)
f(x) = (x-5) * [(x-2)^2 + 1]

Now we have a polynomial function f(x) of least degree with real coefficients and zeros of 5, 2-i, and 2+i:
f(x) = (x-5) * [(x-2)^2 + 1]

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Answer:

Let x be the length of Danika's old running route in miles.

Then, her new running route can be represented by x + 4, since it is 4 miles longer than her old route.

Step-by-step explanation:

Answer:

[tex]\frac{62}{9}[/tex] or  6.8888889

Step-by-step explanation:

The explanation is on the attachment below

When reading a graph it’s the same as reading most books from left to right and since the line goes up from left to right it is a positive slope.

The probability of drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time is approximately 0.00012, or 0.012%.

To determine the probability of drawing three sevens in a row from a standard deck of cards without replacement, we can use the following method:

Step 1: Identify the total number of cards in a standard deck. A standard deck has 52 cards (13 ranks and 4 suits).

Step 2: Determine the number of sevens in the deck. There are 4 sevens (one from each suit).

The probability of drawing a seven from a standard deck of 52 cards is 4/52 or 1/13, since there are four sevens in the deck. After the first seven is drawn, there are 51 cards left in the deck, of which three are sevens. So the probability of drawing a second seven is 3/51. Similarly, after the second seven is drawn, there are 50 cards left in the deck, of which two are sevens. So the probability of drawing a third seven is 2/50.


Step 3: Calculate the probability of drawing the first seven. This would be the number of sevens divided by the total number of cards:
P(1st Seven) = 4/52

Step 4: After drawing the first seven, there are now 51 cards left in the deck and only 3 sevens remaining. Calculate the probability of drawing the second seven:
P(2nd Seven) = 3/51

Step 5: After drawing the second seven, there are now 50 cards left in the deck and only 2 sevens remaining. Calculate the probability of drawing the third seven:
P(3rd Seven) = 2/50

Step 6: To find the probability of all three events happening in a row, multiply the individual probabilities:
P(Three Sevens) = P(1st Seven) * P(2nd Seven) * P(3rd Seven) = (4/52) * (3/51) * (2/50)

Step 7: Calculate the result:
P(Three Sevens) = (4/52) * (3/51) * (2/50) = 0.0012 (approximately)

The probability of drawing three sevens in a row from a standard deck of cards without replacement is approximately 0.0012, or 0.12%.

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The value of function f(- 3) for the piece-wise function is,

⇒ f (- 3) = - 1

We have to given that;

The piece-wise function is,

f (x) = (x + 2) ; if x < 2

      = (x + 1) ; if x ≥ 2

Hence, At x = - 3;

Function is,

⇒ f (x) = x + 2

Hence, Substitute x = - 3;

⇒ f (- 3) = - 3 + 2

⇒ f (-3) = - 1

Thus, The value of function f(- 3) for the piece-wise function is,

⇒ f (- 3) = - 1

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(a) First step of implicit differentiation:
-0.82dP/dt = dq/dt
The equation that results from differentiating each side of the equation with respect to P is:
-0.82 - 0.82P(d^2q/dP^2) = (dQ/dP)(dP/dt)/(dq/dt)
To find the elasticity of demand, we need to use the formula:
E = (dQ/Q)/(dP/P)
We can rewrite this as:
E = (dQ/dP) * (P/Q)
We know that dQ/dP = -0.82P(d^2q/dP^2), so we substitute that into the formula:
E = (-0.82P(d^2q/dP^2)) * (P/q)
Simplifying this expression, we get:
E = -0.82P^2(d^2q/dP^2)/q

(b)  We can solve the original equation for q by dividing both sides by -0.82:
q = (-1/0.82)P + D
Taking the derivative of q with respect to P, we get:
dq/dP = -1/0.82
We can use this result to calculate the elasticity of demand using the formula:
E = (dQ/dP) * (P/Q)
Substituting the values we found, we get:
E = (-1/0.82) * (P/((-1/0.82)P + D))
Simplifying this expression, we get:
E = -1/(P/((-1/0.82)P + D))
E = -1/((D/P) - 1.22)

(a) Interpretation: The elasticity of demand is a measure of how much the quantity demanded changes in response to a change in price. If E > 1, demand is considered elastic, meaning that a small change in price will result in a large change in quantity demanded. If E < 1, demand is considered inelastic, meaning that a change in price will result in a small change in quantity demanded. If E = 1, demand is unit elastic, meaning that a change in price will result in an equal proportional change in quantity demanded.
(b) Interpretation: The elasticity of demand in this case depends on the values of D and P. If D is relatively small compared to P, then the elasticity of demand will be close to -1.22, which is the upper limit of the elasticity. If D is relatively large compared to P, then the elasticity of demand will be close to zero, which means that demand is very inelastic.

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