Nina sells 95% of her cookies at a bake sale. She baked 120 cookies. How many did she sell?

(a) (i) dne (ii) -6 (iii) -6

(b) (i) n-1 (ii) n

(c) The limit exists only for whole number values of 'a.'

(a) (i) In this case, the limit does not exist because the function is not defined for x approaching -6 from the left side. Therefore, the answer is "dne" (does not exist).

(a) (ii) When approaching -6 from either the left or the right side, the value of x remains -6. Thus, the limit is -6.

(a) (iii) Similar to the previous case, when approaching -6.2 from either the left or the right side, the value of x remains -6.2. Therefore, the limit is -6.2.

(b) (i) When approaching a whole number n from the left side, the value of x approaches n-1. Hence, the limit is n-1.

(b) (ii) When approaching a whole number n from either the left or the right side, the value of x approaches n. Therefore, the limit is n.

(c) The limit of x exists only for whole number values of 'a.' This is because the greatest integer function is defined only for whole numbers, and as x approaches any whole number, the value of x remains the same. For non-whole number values of 'a,' the function is not defined, and therefore, the limit does not exist.

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Answer:

$300

Step-by-step explanation:

3/4 = 0.75

1200 * 0.75 = 900

1200 - 900 = 300

Best of Luck!

Answer:

900$

Step-by-step explanation:

if you divide $1200 into four sections it equals up to300 and then multiply 300 by 3 equals $900

Answer:

115

Step-by-step explanation:

answer is in photo above

Let's solve this problem using a system of equations. Let's assume the cost of one hat is represented by 'h' and the cost of one bandana is represented by 'b'.

According to the given information:

The cost of two hats and three bandanas is $114.25:

2h + 3b = 114.25 -- Equation 1

The cost of five hats and two bandanas is $166.0:

5h + 2b = 166.0 -- Equation 2

We can now solve this system of equations to find the values of 'h' and 'b'.

To eliminate 'b', we can multiply Equation 1 by 2 and Equation 2 by 3:

4h + 6b = 228.50 -- Equation 3

15h + 6b = 498.00 -- Equation 4

Subtracting Equation 3 from Equation 4, we get:

15h + 6b - (4h + 6b) = 498.00 - 228.50

11h = 269.50

Dividing both sides by 11:

h = 269.50 / 11

h ≈ 24.50

Therefore, the cost of one hat is approximately $24.50.

The correct answer is (D) $24.50.

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The intersection point of two lines are (-4 , -19)

The intersection point are those point where two line met of cut each other are called intersection point.

the given line of equation are

y = 5x + 1

y = 2x - 11

On solving these two equation we get the values as follow,

value of x = -4

value of y = -19

hence by this we can say the the intersection point of the above lines are

( -4 , -19 )

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Answer:

36 and 108

Step-by-step explanation:

the red lines indicate the sides are equal making it an isosceles triangle the angles opposide the sides are equal so x^2=5x+6 with guess and check I got x=6 and 6x6 is 36 and 5(6)+6 is 36 now to find the last angle, angle f just do 180- (36+36) you get 108

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

rational number is the number that can change to fraction but irrational number can't

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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(2/3)x = 7 + 2

(2/3)x = 9

2x = 9 × 3

x = 27/2

:. x = 13 1/2

Answer:

2 + (3/4)

Step-by-step explanation:

4 + (2/4) - (1 + (3/4))

3 + (2/4) - (3/4)

3 - (1/4)

2 + (3/4)

Answer:

2 and 3/4

Step-by-step explanation:

well start with 4 2/4 and turn it into 18/4 then take 1 3/4 and turn it into 7/4

18/4-7/4=11/4

11/4 is equal to 2 3/4

If you have a required return of 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, you would be willing to pay approximately $206,595.71 for this investment.

To determine the value you would be willing to pay for this investment, we can use the concept of present value. The present value of an investment is the current worth of the future cash flows it will generate. In this case, the investment will pay you $800 a month for 40 years.

To calculate the present value, we can use the formula:

\(PV = CF / (1 + r)^n\)

Where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods.

In this case, the cash flow is $800 per month, the required return is 6% per year (or 0.06/12 = 0.005 per month), and the number of periods is 40 years * 12 months = 480 months.

Plugging these values into the formula, we have:

PV = $800 / \((1 + 0.005)^(480)\)

Calculating this expression, we find that the present value is approximately $206,595.71. Therefore, you would be willing to pay approximately $206,595.71 for this investment to achieve your required return of 6% per year, compounded monthly.

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The weight of the draft horse is \(10^6\) times the weight of the paper clip.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Weight of the paper clip = \(10^{-3}\)

Weight of the draft horse = 10³

Now,

Weight of the draft horse.
= \(10^6\) x Weight of the paper clip

= \(10^6\) x \(10^{-3}\)

= \(10^6\)  x 1/10³

= 10³

Thus,

The weight of the draft horse is \(10^6\) times the weight of the paper clip.

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Answer:

the answer is 6

True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.

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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.

the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.


The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.

Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.

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The image shows a square with a circle cut out of it.

We need to compute the area of the square and subtract the area of the circle to find the shaded area.

The area of a square of side length x is:

We are given the side length of x = 10 ft, thus:

The area of a circle of radius r is given by:

The circle inside the square has a diameter of d=10 ft, thus its radius is r = 10/2 = 5 ft. Calculating the area:

Using π=3.14:

Now, subtracting areas:

Rounding to the next integer, the required area is approximately 22 square ft

Choice: 22 square ft

Answer:

yaaaa

Step-by-step explanation:

Charlie must earn at least 125 tickets in the last game tο win the big prize.

A linear inequality is a mathematical statement that compares twο expressiοns using the symbοls < (less than), > (greater than), ≤ (less than οr equal tο), οr ≥ (greater than οr equal tο), and where bοth expressiοns are linear functiοns οf the same variables. It describes range οf values that the variables can take while satisfying the inequality.

Let x be the number οf tickets that Charlie must earn in the last game tο win the big prize.

The tοtal number οf tickets Charlie has won so far is the sum οf the tickets frοm all the games he has played:

95 + 115 + 90 + 75 = 375.

Tο win the big prize, Charlie must earn at least 500 tickets in tοtal.

Therefοre, we can write the fοllοwing inequality tο sοlve fοr the pοssible number οf tickets, x:

375 + x ≥ 500

Simplifying the inequality:

x ≥ 500 - 375

x ≥ 125

Therefore, Charlie must earn at least 125 tickets in the last game to win the big prize.

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The constant in the given expression is

C. 9

In a mathematical expression, a constant is a value that does not change and remains the same throughout the expression or equation.

It is a fixed numerical value, coefficient, or term that is independent of the variable(s) in the expression.

For example, in the expression 15x^2 + 2x + 9, the constant is 9, as it remains the same regardless of the value of x.

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Answer:

x = 1.25, y = 1.75

Step-by-step explanation:

The smaller and larger triangles are similar triangles. (the 2 triangles have the same angles).

We know that the smaller triangle has length 8 for it's bottom side when the larger triangle has length 10. This means the scale factor between the 2 is 10 / 8 which is 1.25. Therefore by multiplying the side lengths of the smaller triangle by 1.25 we get the side lengths of the larger triangle.

5 * 1.25 = 6.25

7 * 1.25 = 8.75

However we don't want the whole side lengths we want x and y, We need to subtract 5 and 7 respectively from the lengths of the larger triangles.

Therefore the lengths must be: 6.25 - 5 = 1.25

and 8.75 - 7 = 1.75

Therefore x and y equal 1.25 and 1.75

The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.

The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample

p-hat = number of purple skittles / total number of skittles in sample

In this case, we have

Number of purple skittles = 72

Total number of skittles in sample = 300

Therefore,

p-hat = 72/300 = 0.24

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The shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.

(c) When the tax funds are assumed to be gone without any goods or services purchased or government employees paid, it implies that the tax revenue is completely removed from the economy. In this case, the impact on the steady state levels of capital per worker and consumption per worker would depend on the specific economic model and assumptions.

Generally, the removal of tax revenue would lead to a reduction in both capital per worker and consumption per worker. The exact magnitude of the impact would depend on various factors, such as the marginal propensity to consume and the saving behavior of individuals. In steady state, the reduction in capital per worker could lead to lower productivity and potentially lower output per worker, affecting the standard of living.

To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per worker and consumption per worker on the y-axis and time or steady state on the x-axis. The diagram would show a downward shift in both the capital per worker and consumption per worker curves, indicating a decrease due to the removal of tax revenue.

(d) When the tax funds are used by the government to implement plans that increase the growth rate of labor-augmenting technological change to 3% per year, it implies that the tax revenue is directed towards productivity-enhancing investments or policies. In this case, the impact on the steady state levels of capital per effective worker, output per effective worker, and consumption per effective worker can be analyzed.

The increase in the growth rate of labor-augmenting technological change would lead to higher productivity and potentially higher output per effective worker in steady state. This increase in output per effective worker could also translate into higher consumption per effective worker, depending on the saving and consumption behavior.

To sketch a diagram showing the impact of this shock, you would typically have the levels of capital per effective worker, output per effective worker, and consumption per effective worker on the y-axis and time or steady state on the x-axis. The diagram would show an upward shift in the output per effective worker curve, indicating an increase due to the improved technological change.

Overall, the shock in part (c) leads to a decrease in capital per worker and consumption per worker, potentially affecting the standard of living. In contrast, the shock in part (d) leads to an increase in output per effective worker, which can positively impact the standard of living.

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Answer:

The area of the circle is 314 inches

Step-by-step explanation:

Area if a circle = πr²

r = radius

r= d/2

r=20 /2

r=10 inches

Area =3.14×10²

= 3.14×100

=314 inches

Answer:

314 in. cubed

Step-by-step explanation:

The formula to find the area of a circle is:

A= πr²

Pi is 3.14 so substitute that in

A= 3.14(r)²

The radius is 10 because the radius is half of the diameter.  Half of 20 is 10.  So substitute that in the radius symbol.

A= 3.14(10)²

Square 10, which is 10 times 10.  10 times 10 equals 100.

A= 3.14(100)

100 times 3.14 is 314 because 100 has two zeroes which means you move the decimal point in 3.14 two places to the right.  It gets you 314.0 which is just 314.

A= 314

The equation of line B in the form y = mx + c is: y = (-10/7)x - 16/7.

To determine the equation of line B, we need to find its slope (m) and y-intercept (c) based on the given information.

Looking at the graph, we see that point P lies on line A, and line B is parallel to line A. Parallel lines have the same slope. So, to find the slope of line B, we can use the slope of line A.

From the graph, we observe that line A passes through the points (-2, 4) and (5, -6). We can calculate the slope (m) of line A using the formula:

m = (y2 - y1) / (x2 - x1)

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

m = (-6 - 4) / (5 - (-2))

= (-10) / (7)

= -10/7

Now that we have the slope (m) of line B, we need to determine the y-intercept (c). Since line B passes through point P, which is (-3, 2), we can substitute these values into the slope-intercept form equation:

y = mx + c

Substituting (-3, 2) and -10/7 for (x, y) and m, respectively, we get:

2 = (-10/7)(-3) + c

Simplifying the equation, we have:

2 = 30/7 + c

To isolate c, we subtract 30/7 from both sides:

2 - 30/7 = c

Multiplying the terms, we have:

14/7 - 30/7 = c

Simplifying further, we get:

-16/7 = c

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Answer:

  False

Step-by-step explanation:

You want to know if it is true that the graph of a rational function cannot cross a horizontal asymptote.

Once a function is on its final approach to an asymptote, it will approach, but not cross, that asymptote.

The function may have a variety of behaviors prior to that point, so may cross the horizontal asymptote one or more times before its final behavior is established.

An example with the asymptote y = 0 is attached.

<95141404393>

Answer:2 AND 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=-4±√23

Answer:

x=-4±√23

Step-by-step explanation:

Answer:

Fraction = \(\frac{1}{20}\) and Decimal = 0.05

Step-by-step explanation:

Percent means, some number over a hundred.

in this case we have 5%

\(\frac{5}{100} = \frac{1}{20}\)

and for decimal form we just move the decimal 2 places to the left because our denominator is a 100 and we get 0.05.