The area of a rectangular parking lot is 21x2 - 44x + 15. The width of the
parking lot is 3x - 5. What is the length of the parking lot?

The equation of the circle with a radius of 5 and center at (2, 3) in cartesian form is (x - 2)^2 + (y - 3)^2 = 25.

For the described curve, a circle with a radius of 5 and center at (2, 3), it would be more easily given by a **cartesian equation**.

A cartesian equation represents a curve in terms of x and y coordinates, which aligns well with the standard representation of a circle. The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2.

In this case, the center of the circle is (2, 3), and the radius is 5. Plugging these values into the equation, we get:

(x - 2)^2 + (y - 3)^2 = 5^2.

Expanding and simplifying the equation further, we have:

(x - 2)^2 + (y - 3)^2 = 25.

Thus, the equation of the circle with a radius of 5 and center at (2, 3) in cartesian form is:

(x - 2)^2 + (y - 3)^2 = 25.

Using the cartesian equation allows us to directly relate the x and y coordinates to represent the circle's shape and position on a standard coordinate plane.

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Answer:

Should be 251.3 cm^3

Step-by-step explanation:

Use the formula for volume of cylinder

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

hello

to solve this problem, we need to draw the

We are to use the method of undetermined coefficients to solve the given nonhomogeneous system.

We have:x' = [1 3 31] x − [−2t² t 3]

The homogeneous system is x′= [1 3 31] x

This system has characteristic equation as: r³ - 35r² + 290r - 620 = 0

Solving for r, we get:

r = 2 (double root) and r = 31

Clearly, the solution of the homogeneous system is

xh = (c1 + c2t + c3t²)e²t + c4e³¹t -------------------(1)

Next, we have to find the particular solution of the given system.

The given non-homogeneous system can be represented in the form:

x' = Ax + f(t) = [1 3 31] x − [−2t² t 3]

Hence, we have to find a solution of the form:

xp = u(t) + v(t) t² + w(t) t³

Substituting xp in the given system and solving for u, v, and w,

we get:

u(t) = 2t³ + 33t² + 28tu(t) = − 2t³ − 2t² + 6t

Substituting these values in xp, we get:

xp = (2t³ + 33t² + 28t)e²t − (2t³ + 2t² − 6t) e³¹t + (t³ − 15t² + 44t) te²t

Thus, the general solution of the nonhomogeneous system is given by:

x = xp + xh = (2t³ + 33t² + 28t)e²t − (2t³ + 2t² − 6t) e³¹t + (t³ − 15t² + 44t) te²t + (c1 + c2t + c3t²)e²t + c4e³¹t.

Note: The method of undetermined coefficients is not always the best method to find the particular solution of a non-homogeneous system.

It is advisable to use matrix exponential or Laplace transform method to solve such a system.

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Answer:

A= (3*X - 6\(\sqrt{x}\))/(X-4)

A=(3*2 - 6\(\sqrt{2}\))/(2-4)= -3+3\(\sqrt{2}\)

A=(3*4 - 6\(\sqrt{4}\))/(4-4) Unknown

Step-by-step explanation:

The statement which most likely represent "dependent-samples" is (d) study which compares standardized "test-scores" before and after course is taken.

The scores obtained before and after are linked, as they are obtained from the same group of individuals, and are therefore dependent samples.

For example, suppose a group of students is given a standardized test before and after taking a preparation course.

The scores obtained before the course are likely to be related to the scores obtained after the course, as they are both measures of the same group of students.

If the course has a significant impact on the scores, the before-and-after scores will likely be correlated, and the samples will be dependent.

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

Which of the following are most likely to be dependent samples?

(a) A study that compares the mean wait times at two different hospital emergency rooms

(b) A study that compares the salaries earned by men and women in the same job position

(c) A study that compares the weight gain for puppies who eat two different brands of food

(d) A study that compares standardized test scores before and after a course is taken.

Given:

The initial population is p = 26 million.

The decreasing percentage is r = 15% each year = 0.15.

The objective is to write the sequence of population after 4 years.

Explanation:

The general formula of population decrease is,

The population in the 1st-year can be calculated by substituting t=1 in equation (1).

The population in the 2nd year can be calculated by substituting t=2 in equation (1).

The population in the 3rd year can be calculated by substituting t=3 in equation (1).

Hence, the population for the first 4 years will be,

26million,

22.1million,

18.785million,

15.967255million.

The minimum branching factor of a B-tree is the minimum number of children a node can have in order to keep the tree balanced.

What is a B-tree?

A self-balancing search tree is the B-Tree. It is assumed that everything is in the main memory in the majority of the other self-balancing search trees (such AVL and Red-Black Trees).

We must consider the vast quantity of data that won't fit in the main memory in order to comprehend the utilisation of B-Trees. Data is read from the disc in the form of blocks when the number of keys is high. In comparison to the access time to main memory, disc access time is quite long. Reducing the amount of disc accesses is the major goal of employing B-Trees. The majority of tree operations, such as search, insert, delete, max, min, etc., call for O(h) disc accesses, where h is the tree height. A fat tree is the B-tree.

By packing as many keys as you can into each B-Tree node, the height of B-Trees is maintained to a minimum. The disc block size is often maintained at the same as the B-Tree node size. In comparison to balanced Binary Search Trees like the AVL Tree, Red-Black Tree, etc., the B-low tree's height results in a considerable reduction in the overall number of disc visits for the majority of operations.

b-trees what is the relation between the minimum branching factor and the minimum degree of a b-tree? which of the following are legal b-trees for when the minimum branching factor.

It is also known as the minimum degree of the B-tree. The minimum degree of a B-tree must be greater than or equal to the minimum branching factor.

The following are all legal B-trees for when the minimum branching factor is 3:

- 3-3-3-3 B-tree
- 2-3-3-4 B-tree
- 2-3-4-5 B-tree
- 3-4-5-6 B-tree
- 2-4-5-6 B-tree

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Answer:

546

Step-by-step explanation:

Each square inch is equal to 6.5 square centimeters so you can multiply

84 × 6.5 = 546So, the area is 546 square centimeters.

Hope this helps =>

Answer:

\(541.93\ cm^2\)

Step-by-step explanation:

Step 1:  Determine the area in square centimeters

\(84\ in^2 * \frac{(2.54\ cm)^2}{in^2}\)

\(84\ in^2 * \frac{(2.54)^2 * (cm)^2}{in^2}\)

\(84\ in^2 * \frac{6.4516\ cm^2}{in^2}\)

\(541.9344\ cm^2\)

Answer: \(541.93\ cm^2\)

The uniform continuous probability for the interval (25 < x < 45) within the uniform distribution U(15, 65) can be found by calculating the proportion of the total range that falls within that interval.

To calculate the probability, we need to determine the length of the interval (45 - 25) and divide it by the length of the entire range (65 - 15).

Length of the interval: 45 - 25 = 20

Length of the entire range: 65 - 15 = 50

Now, we divide the length of the interval by the length of the entire range to obtain the probability:

Probability = (Length of interval) / (Length of entire range) = 20 / 50 = 0.4

Therefore, the uniform continuous probability for p(25 < x < 45) within the uniform distribution U(15, 65) is 0.4, rounded to one decimal place.

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The block will cover the distance 12m before it stops.

According to Newton's second law of motion, the acceleration a

of a body of mass m is determined by the net force \(F_n_e_t\) acting on it:

\(F_n_e_t\)  = ma.

The mass of a block, m = 8 kg

The initial speed of the block on rough horizontal surface , u = 6 m/s

The force of friction, F = 12N

We know that, the Newton's 2nd law: \(F_n_e_t\)  = ma.

Therefore, its final velocity is zero, v = 0

Since the only force that is acting on the body along the horizontal direction is the kinetic frictional force

\(F_n_e_t\)  = ma. (\(F_n_e_t\)  is acting in opposite direction to that of object motion)

a = \(\frac{f_n_e_t}{m}\) = \(\frac{-12}{8} = -1.5m/s^2\)

Negative sign shows that it is in the opposite direction to that of initial velocity.

By using the third kinematic equation, we get:

\(v^2=u^2+2as\\\\= > s = \frac{0-6^2}{2(-1.5)}\\ \\s = \frac{36}{3} = 12m\)

Therefore, the block will cover the distance 12m before it stops.

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Explanation:

Let's solve the first equation for y

4x - 2y = 6

4x-6 = 2y

2y = 4x-6

y = (4x-6)/2

y = (4x/2) - (6/2)

y = 2x - 3

After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3

Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).

Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.

You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.

-------------------------------

Here's another approach using substitution

4x - 2y = 6 ... start with the first equation

4x - 2( y ) = 6

4x - 2( 2x-3 ) = 6 .... replace y with 2x-3; ie plug in y = 2x-3

4x - 2(2x) - 2(-3) = 6

4x - 4x + 6 = 6

0x + 6 = 6

0 + 6 = 6

6 = 6

We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.

Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.

The amount of Protein intake is 900 kilocalorie.

We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.

Wе have to find out the amount of protein intake.

Percentage of students affected are -  \(\frac{x}{n} \times 100\)

In the question given -

Let the amount of Protein intake be y.

Then -

45 = y % of 2000

45 = \(\frac{y}{2000} \times100\)

y = \(\frac{45\times2000}{100}\)

y = 900 Kilocalorie

Hence, the amount of Protein intake is 900 kilocalorie.

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Answer:

  (a)  x^2 +4x +3

Step-by-step explanation:

The attachment shows the synthetic division. The quotient is ...

  x^2 +4x +3

_____

Additional comment

Please make sure your math posts include all necessary math symbols and formatting. Some Brainly input methods seem to drop + signs and/or make spacing adjustments that render questions indecipherable. It is helpful if you separate answer choices with punctuation, letter designators, and/or spacing (one per line, for example).

Answer:a

Step-by-step explanation:

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

9. The truth value of the complex statement (A⋅Y)v(−Z⋅C) is true.

10. The truth value of the complex statement ∼(X∨∼B)⋅(∼Y∨A) is false.

Let's determine the truth value of each complex statement based on the given information:

(A⋅Y)v(−Z⋅C)

Given: A, B, C are true, and X, Y, Z are false.

(A⋅Y)v(−Z⋅C) = (true⋅false) v (true⋅true) (since −Z⋅C is true when Z is false and C is true)

= false v true

= true

Therefore, the truth value of the complex statement (A⋅Y)v(−Z⋅C) is true.

∼(X∨∼B)⋅(∼Y∨A)

Given: A, B, C are true, and X, Y, Z are false.

∼(X∨∼B)⋅(∼Y∨A) = ∼(false∨true)⋅(true∨true) (since ∼X is true when X is false, and ∼B is false when B is true)

= ∼true⋅true

= false⋅true

= false

Therefore, the truth value of the complex statement ∼(X∨∼B)⋅(∼Y∨A) is false.

9. The truth value of the complex statement (A⋅Y)v(−Z⋅C) is true.

10. The truth value of the complex statement ∼(X∨∼B)⋅(∼Y∨A) is false.

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Answer:

1. 16-x-x-x-x = 0

   x = 4

2. 18-y-y-y-y-y-y-y-y-y = 0

   y = 2

3. 27-x-x-x =0

   x = 9

4. 100-y-y-y-y-y-y-y-y-y-y = 0

   y = 10

Answer:

slope c =1

Step-by-step explanation:

slope for line (y2-y1)/(x2-x1)

slope of line a = (-3-3)/(3-(-3))

slope of  line a = -6/6 = -1

if line c is perpendicular to line a, so relationship for slops are

(slope a) *(slope c)= -1

(-1)*(slope c) = -1

slope c =1

Answer:

mc = 1

Step-by-step explanation:

Answer:

Answer choices?

Step-by-step explanation:

Answer:

problem one

x = 3- 5y/3

y = 9/5 - 3x/5

problem 2

x= -12 + 10y/3

y= 18/5 + 3x/10

Step-by-step explanation:

(a) Number of ways to line up 10 members =10! =3,628,800 number of ways so that VP and president are next to each other 2.9!

(b) To line up the ten people if the VP must be beside the president in the photo 725,760 ways.

(c) To line up the ten people if the president must be next to the secretary and the VP must be next to the treasure is:  161,280 ways.

a). To line up the ten people with no restrictions in arrangement; we have;

n! = 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 3,628,800 ways.

b). To line up the ten people if the VP must be beside the president in the photo;

then, there are 9 entities as the VP and president are considered as one entity. However, there are 2! ways to arrange the president and vp, we have:

=> 9! × 2!

=  725,760 ways.

c). To line up the ten people if the president must be next to the secretary and the VP must be next to the treasure we have:

= 8! × 2! × 2!

= 161,280 ways.

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The given question is incomplete, complete question is:

ten members of a club are lining up in a row for a photograph. the club has one president, one vp, one secretary, and one treasurer. (a) how many ways are there to line up the ten people? (b) how many ways are there to line up the ten people if the vp must be beside the president in the photo? (c) how many ways are there to line up the ten people if the president must be next to the secretary and the vp must be next to the treasurer?

The marginal cost of producing one more unit of the product when x = 100 is $150 per unit. To find the instantaneous rate of change (or the marginal cost) of c with respect to x when x = 100, we need to calculate the derivative of the cost function c(x) with respect to x and evaluate it at x = 100.

Let's assume that we have the cost function c(x) = 0.5x^2 + 50x + 1000, where x is the number of units produced. To find the derivative of this function, we need to use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to our cost function, we get:

c'(x) = d/dx (0.5x^2 + 50x + 1000)
     = 1x^(2-1) + 50x^(1-1) + 0
     = x + 50

Now, we can evaluate this derivative at x = 100 to find the marginal cost:

c'(100) = 100 + 50
       = 150

Therefore, the marginal cost of producing one more unit of the product when x = 100 is $150 per unit. This means that if the company produces one more unit of the product, it will cost them $150 more than the cost of producing the previous unit. The significance of the marginal cost will be explained in a future chapter, but for now, it is important to understand that it is a crucial concept in economics and business decision-making.

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its the first option.

tiles of X and tiles of 1 are different

3 tiles of "X" = 3X

3 tiles of " 1 " = 3

option 3 does not mean 3X, it just means 3X + 3

Answer:

If it's the other way around which is x+3 it would be

Step-by-step explanation:

1=X

&

3 ones

x-1-1-1

Hope that helps as well 0_0

The number of variables in a data collection whose values can fluctuate while others remain fixed is referred to as a degree of freedom. So, the third choice is the right one.

A variable that indicates a quantity being altered in an experiment is known as an independent variable. In equations, x is frequently used to denote the independent variable. A variable that indicates a quantity being altered in an experiment is known as an independent variable. Values that fluctuate in relation to one another are independent and dependent variables in mathematics.

Given.

The number of variables in a data collection whose values can fluctuate while others remain fixed is referred to as a degree of freedom. So, the third choice is the right one.

In other words, the number of values that can change in a statistical calculation is referred to as the degree of freedom.

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Answer:

9.9225 E 34.

E = exponent

= 9.9225 x 10^34

Step-by-step explanation:

Answer:

=

64 / 7x -2

Step-by-step explanation:

You multiply 16 and 4/7 than you take away 2 I think im bad at this-

Answer:

First, we will find the coordinates of ABCD:

A: (1,1)

B: (1,4)

C: (4,6)

D: (5,3)

Now we will find the coordinates of PQRS:

P: (5,5)

Q: (8,6)

R: (7,4)

S: (7,2)

Have a great day!!

Pleas rate and mark brainliest!!

To find a coordinate of a vertice, we see the point that the x axis and the y axis intersect. And it's written in the form of (x;y - x axis first, y axis second)

Polygon 1 :
B vertice : (1;4)
A vertice : (1;1)
C vertice : (4;6)
D vertice : (5;3)

Polygon 2 :

P vertice : (5;5)
Q vertice : (8;6)
R vertice : (7;4)
S vertice : (7;2)