Is -2.5 greater than or less than 2.1?

Answer:

Step-by-step explanation:

42 square units

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer:

Option A: $12.50

Step-by-step explanation:

equation being: 62.50/5=12.5

62.50 (total cost of the pizza's) / 5 (total amount of pizza's) = 12.5

otherwise, known as: $12.50

Hope this helps!

The scale factor k is  k = 3/6 = 1/2 or k = -1/2. But since the dilation takes place with respect to the center of dilation (2, -1), which is inside the smaller triangle, the scale factor should be positive. Hence the scale factor is 1/2. The correct option is 12.

Let the smaller triangle be the preimage and the larger triangle be the image. The center of dilation is (2, −1).

The coordinates of the vertices of the preimage and the image are shown below.

Preimage:(0,0), (3,0), (0,4)

Image:(2, −1), (8, −1), (2, 11)

Let the scale factor be 'k'.

Using the distance formula, the lengths of the sides of the triangles can be calculated as:

Preimage:AB

= 3, BC

= 4, AC

= 5

Image:AB

= 6k, BC

= 8k, AC

= 10k

Since the smaller triangle is dilated to the larger triangle, the scale factor k is greater than 1.

Also, the center of dilation is (2, −1), which means that the dilation takes place with respect to the line x= 2.

Therefore, the distance of the vertices of the smaller triangle from the line x = 2 should be multiplied by the scale factor k to obtain the corresponding vertices of the larger triangle.

Thus, 2 is equidistant from the vertices of the smaller triangle.

Therefore, the horizontal distance of the corresponding vertices of the larger triangle from the line

x = 2 is 2k.

That is, 2k

= 8 − 2

= 6k

= 3 .

The scale factor k is, therefore, k

= 3/6

= 1/2 or k

= -1/2.

But since the dilation takes place with respect to the center of dilation (2, -1), which is inside the smaller triangle, the scale factor should be positive.

Hence the scale factor is 1/2.

The correct option is 12.

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Answer:

irrational

Step-by-step explanation:

well if it goes on forever its irrational

Answer:

-12 and -4

Step-by-step explanation:

-12 + (-4)  = -16

-12 x -4 = 48

Answer:

-4, -12

Step-by-step explanation:

-4 + (-12) = -16

-4 x -12 = 48

Answer:

1. Deep Ocean Currents

2. Deep Ocean Currents

Step-by-step explanation:

Answer:

Graph under 10, only a bit, (0,9) because y = 9

Step-by-step explanation:

The values based on the functions given will be:

1. f(g(9)) = V33 + 3

2. g(f(6)) = 4V6 + 9

3. g(h(1)) = 21

4. h(g(0)) = -6

5. h(S(-2)) = -3

6. f(h(5)) = V18 + 3

7. &(g(1.5)) = 3

8. f(f(-2)) = 2

f(g(9)) = f(4(9) - 3) = f(33) = V33 + 3

g(f(6)) = g(V6 + 3) = 4(V6 + 3) - 3 = 4V6 + 9

g(h(1)) = g(3(1) + 3) = g(6) = 4(6) - 3

h(g(0)) = h(4(0) - 3) = h(-3) = 3(-3) + 3

h(S(-2)) = h(-2) = 3(-2) + 3

f(h(5)) = f(3(5) + 3) = f(18) = V18 + 3

&(g(1.5)) = &(4(1.5) - 3) = &(3) = 3

f(f(-2)) = f(V(-2) + 3) = V(V(-2) + 3) + 3 = V1 + 3 = 2

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Answer: \(\angle F = 44\°\\angle D= 46\°\)

Step-by-step explanation:

The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

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82 students attended the dance.

In algebra, an equation can be expressed as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

An equation is defined as two expressions, connected by an equals sign ("="). The expressions on the two sides of the equals sign are said the "left-hand side" and "right-hand side" of the equation. Assuming this does not reduce the generality, this can be realized by subtracting the right-hand side from both sides.

According to the given problem,

Let the number of students be x,

2.50x + 120 = 325

⇒ 2.5x = 325 - 120

⇒ 2.5x =   205

⇒ x = 82

Hence, 82 students attended the dance.

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The solution of the given system of equation is (-19, 55).

In the given question we have to find the solution to the system of equations:

y = -3x-2 and 5x + 2y = 15

We can solve the system of equation using the substitution method.

In substitution method we have to put the the value of one variable from one equation to the other equation.

We have to equations:

y = -3x-2...................................(1)

5x + 2y = 15.............................(2)

Now putting the value of y from the equation 1 in equation 2

5x + 2(-3x-2) = 15

Now solving the equation using the distribution method.

5x - 6x - 4 = 15

Simplifying

-x - 4 = 15

Add 4 on both side we get

-x = 19

Now the value of x is -19.

Now putting the value of x in equation 1

y = (-3)*(-19)-2

y = 57-2

y = 55

Hence, the solution of the given system of equation is (-19, 55).

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The right question is:

What is the solution to the system of equations y = -3x-2, 5x+2y=15?

The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

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Answer:

1286 meters long

Step-by-step explanation:

421,808 divided by the width of the plot gives you 1,286 meters for the width.

Answer:

I really don't know , I am in 7th grade

Answer:

x = 121°

Step-by-step explanation:

The lower left vertex and 115 are adjacent and supplementary, thus

left vertex = 180° - 115° = 65°

The angle round a point = 360°, so the top vertex is

360° - 304° = 56°

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle, thus

x = 65° + 56° = 121°

Answer:

1.  x =-2, y=6

2. x = 0, y = 0

3. x=2, y=10

Step-by-step explanation:

It will take a long time to explain. If you need explanation, tell me.

Answer:

12/25

Step-by-step explanation:

There were a total of 48 males, so 48/100 = 12/25.

+---------------+------+--------+-------+

|           | Male | Female | Total |

+---------------+------+--------+-------+

| Prefers Dogs  | 36 | 20 | 56   |

+---------------+------+--------+-------+

| Prefers Cats  | 10   | 26 | 36   |

+---------------+------+--------+-------+

| No Preference | 2 | 6  | 8   |

+---------------+------+--------+-------+

| Total         | 48   | 52     | 100   |

+---------------+------+--------+-------+

The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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Average Speed is 23/32 laps per minute.

In the given statement is:

Carlos jogged 5 3/4 laps around the school track in 8 minutes.

What is Average speed?

Average Speed is calculated by dividing the total distance travelled by the time interval. For example, Someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph)

Now, According to the Question:

5 3/4laps = 23/4 laps

23/4 ÷8

=23/4 × 1/8

=23/32

So, 23/32 laps per minute

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Answer:

2.6+7.4 or 2.4+7.6

Step-by-step explanation:

Both of the above equals to 10!

To locate the centroid y of the shaded area, we need to evaluate the integrals using Simpson's rule.

Let's denote the shaded area as A, and the function y = 0.5e^x^2.

The centroid y of the shaded area A is given by the formula:

y = (1 / A) * ∫(y^2) dx

Using Simpson's rule, we can approximate the integral by dividing the interval into subintervals and using a weighted average of function values.

Let's define the interval of integration as [a, b]. In this case, the interval is not specified, so we'll assume it to be from -∞ to +∞.

Using Simpson's rule, the approximation for the integral is:

∫(y^2) dx ≈ (1 / 3) * h * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + ... + 2f(x_n-2) + 4f(x_n-1) + f(x_n)]

where h is the step size (equal to (b - a) / n) and n is the number of subintervals.

To apply Simpson's rule, we need to evaluate the function y^2 = (0.5e^x^2)^2 = 0.25e^(2x^2) at the given points x_i.

The weights for Simpson's rule are 1, 4, 2, 4, 2, ..., 2, 4, 1.

We can then calculate the centroid y as:

y = (1 / A) * (1 / 3) * h * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + ... + 2f(x_n-2) + 4f(x_n-1) + f(x_n)]

However, since the interval of integration is not specified, we cannot perform the calculations without a defined range.

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Answer:

first question angle J. Because corresponding sides are equal. Second is 3rd one by SSS. thank me later. ❤️

Answer: 21

Step-by-step explanation:

Addressing issue at hand, we can state that the correct linear equation comparison symbol to the box. 10.09 10.9 f < = > is => 10.09 < 10.9

The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

the correct comparison symbol to the box.

10.09 10.9

< = >

10.09 < 10.9

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Answer:

The latest time she can leave is 6:56 A.M.

Step-by-step explanation:

Just trust me. :)

Answer:

Step-by-step explanation:

Answer:

The answer is actually not an option here. The answer is y=-1/3x+16

Answer:

1)8.5 units

2)7 units

Step-by-step explanation:

To find the distance between two points use distance formula.

1) ( 3 , 1)   &  (6 , 9)

     \(\sf \boxed{\bf Distance = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}}\)

                \(\sf AB = \sqrt{(3-6)^2+(1-9)^2}\\\\~~~~~ = \sqrt{(-3)^2+(-8)^2}\\\\~~~~~ =\sqrt{9+64}\\\\~~~~~=\sqrt{73}\\\\\)

                      =  8.5

_________________________________________________

2)(3 , 8) & (8 , 3)

      \(\sf AB = \sqrt{(3-8)^2+(8-3)^2}\\\\\)

            \(\sf =\sqrt{(-5)^2+(5)^2}\\\\=\sqrt{25+25}\\\\=\sqrt{50}\\\\=7\)