[2(5 – 4) + 6(7 – 3)] ÷ 2

There are 266 number of  ways to park 3 distinct cars in 9 consecutive parking slots such that at least one parking slot remains vacant between any two cars.

To determine the number of ways to park 3 distinct cars in 9 consecutive parking slots such that at least one parking slot remains vacant between any two cars, we need to consider the possible arrangements.

Let's analyze the scenario:

1. All three cars are parked in adjacent slots

In this case, there are 7 possible positions where the first car can be parked (as it needs at least one vacant slot on the right side), 6 possible positions for the second car (as it also needs one vacant slot on the right side), and the third car will occupy the remaining slot.

Total arrangements for Case 1 = 7 * 6 = 42.

2. One vacant slot between the cars

In this case, there are 7 possible positions where the first car can be parked (as it needs at least one vacant slot on the right side).

After parking the first car, there will be 5 remaining slots where the second car can be parked (one vacant slot between the first and second car).

The third car will occupy one of the remaining 4 slots.

Total arrangements for Case 2 = 7 * 5 * 4 = 140.

3. Two vacant slots between the cars

In this case, there are 7 possible positions where the first car can be parked (as it needs at least one vacant slot on the right side).

After parking the first car, there will be 4 remaining slots where the second car can be parked (two vacant slots between the first and second car).

The third car will occupy one of the remaining 3 slots.

Total arrangements for Case 3 = 7 * 4 * 3 = 84.

Total number of ways = Total arrangements for Case 1 + Total arrangements for Case 2 + Total arrangements for Case 3

Total number of ways = 42 + 140 + 84 = 266.

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The general solution of the differential equation is: y = y_h + y_p

= c_1 cos(θ) + c_2 sin(θ) + (1/2) ln|cos(θ)| cos(θ) - (1/2) tan(θ) csc(θ) sin(θ) - (1/2) ln|cos(θ)| sin(θ) - (1/2) sec(θ).

The characteristic equation of the homogeneous part of the differential equation is given by:

r^2 + 1 = 0

which has the roots r = ±i. Thus, the general solution of the homogeneous part is:

y_h = c_1 cos(θ) + c_2 sin(θ)

To find the particular solution using the method of variation of parameters, we assume that:

y_p = u(θ)cos(θ) + v(θ)sin(θ)

where u(θ) and v(θ) are functions to be determined.

Taking the first and second derivatives of y_p, we get:

y'_p = u' cos(θ) - u sin(θ) + v' sin(θ) + v cos(θ)

y''_p = -u cos(θ) - 2u' sin(θ) - v sin(θ) + 2v' cos(θ)

Substituting these expressions into the differential equation, we get:

-u cos(θ) - 2u' sin(θ) - v sin(θ) + 2v' cos(θ) + u cos(θ) + v sin(θ) = sec(θ) tan(θ)

Simplifying and collecting like terms, we get:

-2u' sin(θ) + 2v' cos(θ) = sec(θ) tan(θ)

Dividing both sides by 2cos(θ), we get:

u' tan(θ) - v' sec(θ) = (1/2) tan(θ)

Now, we need to find u(θ) and v(θ) such that the left-hand side of the above equation satisfies the integrating factor e^(-ln|cos(θ)|) = |cos(θ)|^(-1). Multiplying both sides of the equation by this integrating factor, we get:

u' sin(θ)/|cos(θ)| - v' = (1/2) tan(θ)/|cos(θ)|

Integrating both sides with respect to θ, we get:

u(θ) = (1/2) ln|cos(θ)| - (1/2) tan(θ)csc(θ) + C1

v(θ) = -(1/2) ln|cos(θ)| - (1/2) sec(θ) + C2

where C1 and C2 are constants of integration.

Therefore, the general solution of the differential equation is:

y = y_h + y_p

= c_1 cos(θ) + c_2 sin(θ) + (1/2) ln|cos(θ)| cos(θ) - (1/2) tan(θ) csc(θ) sin(θ) - (1/2) ln|cos(θ)| sin(θ) - (1/2) sec(θ)

where c_1 and c_2 are arbitrary constants.

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Answer:

The center of the circle is

Step-by-step explanation:

Equation of a circle is given by

where r is the radius

(h, k) is the center of the circle

The center of a circle is given by

( - h , - k)

From the question equation of the circle is

( x + 4)² + ( y - 2)² = 16

Comparing with the general equation above

( h , k) = ( 4 , - 2)

The center of the circle is

( - h , - k) = ( - 4 , -(-2))

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Step 1: Flip the equation.

r+2=2

Step 2: Subtract 2 from both sides.

r+2−2=2−2

2-2=0

Therefore your answer is 0

Answer:I don’t Knowt Try To Answer it yourself

Step-by-step explanation:

Answer:

F- 18 Hz. = 19m 2.

Step-by-step explanation:

The S&P 500 and XYZ Inc. have a positive linear relationship.

The covariance between two variables provides information about the relationship between them, but it does not clearly measure the strength or type of the relationship. A positive covariance means that the variables move in the same direction, while a negative covariance means that the variables move in opposite directions.

In this case, the covariance between the S&P 500 and XYZ Inc. is 6,317.50, which is a positive value. This suggests that there is a positive linear relationship between the two variables, meaning that as the S&P 500 increases, XYZ Inc. also tends to increase, and vice versa. However, to fully understand the relationship between the two variables, it is necessary to calculate other measures, such as the correlation coefficient, which provides a standardized measure of the power and direction of the relationship between two variables.

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The height of the flagstaff by suing trigonometric ratios is found to be 27 m.

Given,

Height of the ladder, AD = 18 m

The distance to the point below the top of a vertical flagstaff where the ladder reaches, CD = 18m

Angle of elevation of flagstaff from the foot of the ladder, ∠ CAB = 60 °

Δ ACD is isosceles triangle.(Image is attached)

∠ ACB = ∠ CAD = 30 °

In △ ABD, by using the trigonometric ratios, we get that:

Sin 30 ° =  BD / AD

1 / 2 = BD / 18

BD = 9 m

So, the height of the flagstaff will be:

BC = BD + DC =9 + 18 = 27 m

Therefore, we get that, the height of the flagstaff by using trigonometric ratios is found to be 27 m.

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Answer:

Step-by-step explanation:

-2

Apply this particular rule of logs:

log a - log b = log a/b

Therefore, log2 (3) - log2 (12) = log2 (3/12) = log2 (1/4)

This last result simplifies to  log2 1 - log2 4 = 0 - 2 = -2

Answer:

-2

Step-by-step explanation:

\(log_2(3)-log_2(12)\)

~Simplify using log properties

\(log_2(\frac{3}{12})\)

\(log_2(\frac{1}{4})\)

~Apply log rules

\(-log_2(4)\)

~Rewrite

\(-log_2(2^2)\)

~Apply log rules

\(-2log_2(2)\)

~Apply log rules

-2 * 1

~Simplify

-2

Best of Luck!

The needed coordinate of Y when the sequence of transformations, R90° ° Tx-axis, is used on  ΔXYZ to make ΔX''Y''Z' is (0, 3)

The process of transformation involves the implementation of a fresh range of mathematical coordinates which are expressed as alternative functions of the initial coordinates.

A rotation 90 can be represented by the formula (x, y) —>  (-y, x)

Note that the there in the question, the coordinate Y is (3, 0)  Of the coordinate is transformed by 90degrees, the given new coordinate will be (0, 3) to (3,0)

So:

3 is the x point.

0 is the y point.

When you replace these two points (switch places) Hence, the x coordinate is 0 and the y coordinate is 3 giving us  (3,0)

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If the coordinates of Y'' are (3, 0), then the coordinates of Y is (0, 3)

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

The sequence of transformations:

This means that we rotate by 90 degrees and we reflect the triangle across the x-axis

The rule of 90° clockwise rotation is (x,y) = (y,-x)

The rule fo rx-axis is (x, -y)

When combined, we have

(x,y) = (y,-x) = (y, x)

using the above as a guide, we have the following:

If the coordinates of Y'' are (3, 0), then the coordinates of Y is (0, 3)

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Answer:

x=10

Step-by-step explanation:

2/3+5/6x=9

5/6x=8 1/3

5/6x=25/3

5x=50

x=10

(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))

To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:

dx / (10 - x) = 0.005 dt

Integrating both sides:

-ln|10 - x| = 0.005t + C

where C is the constant of integration. Solving for x:

|10 - x| = e^(-0.005t - C)

Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:

C = -ln(10)

Therefore, the solution to the differential equation is:

x(t) = 10 - e^(-0.005t - ln(10))

Simplifying:

x(t) = 10(1 - e^(-0.005t))

(b) New bills will make up 90% of the currency in circulation after approximately 461 days.

We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):

9 = 10(1 - e^(-0.005t))

Dividing both sides by 10 and taking the natural logarithm:

ln(0.1) = -0.005t

Solving for t:

t = 200 ln(10) = 460.51

Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.

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Answer:

California

Florida

New York

Washington

Massachusetts

Arizona

Step-by-step explanation:

Answer:

13/25

I hope this is the correct answer.

Answer:

Since each question has 3 choices and only one is correct, the probability of answering a single question correctly is 1/3.

To find the probability of answering all 10 questions correctly, we need to multiply the probabilities of each individual question together, since the events are independent.

Therefore, the probability of acing the test is:

(1/3)^10 = 0.000005904

Or approximately 0.0006%, which is a very small probability.

Step-by-step explanation:

The value of b is -16 and the value of ac is 60 after comparing with the standard equation.

Any equation of the form \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)

We have a quadratic function:

= 3x² - 16x + 20

On comparing with standard function:

b = -16

a = 3

c = 20

ac = 3(20) = 60

Thus, the value of b is -16 and the value of ac is 60 after comparing with the standard equation.

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Y intercepts when x = 0

Based upon this information, the value of the test statistic is 0.23.

The term "test statistic" refers to a quantity obtained from the sample and used in statistical hypothesis testing.

The sample proportion, or ratio of the sample size to the number of "yes" responses (23), would be the test statistic in this situation (100). The sample proportion is computed in the following manner:

The test statistic is p = 23/100, or 0.23.

So, 0.23 is the test statistic. The percentage of dog owners that routinely feed their dogs Woof Chow dog food is represented by this sample estimate.

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To find the truth set of the predicate "6/d is an integer" over the domain of integers (Z), we need to determine all the values of d for which the statement is true. a) Therefore, the truth set of the predicate is {1, 2, 3, 6}. b) the truth set of the predicate is {1, 2}.

First, we note that 6/d can only be an integer if d is a divisor of 6. The divisors of 6 are 1, 2, 3, and 6.
For d = 1, we have 6/1 = 6, which is an integer. For d = 2, we have 6/2 = 3, which is also an integer. For d = 3, we have 6/3 = 2, which is an integer. For d = 6, we have 6/6 = 1, which is an integer. Therefore, the truth set of the predicate is {1, 2, 3, 6}.

To find the truth set of the predicate "1≤x^2 ≤ 4" over the domain of integers (Z), we need to determine all the values of x for which the statement is true. First, we note that x^2 can only be an integer if x is an integer. The integers between 1 and 4 (inclusive) are 1, 2, 3, and 4.

For x = 1, we have 1^2 = 1, which satisfies the predicate. For x = 2, we have 2^2 = 4, which also satisfies the predicate.
For x = 3, we have 3^2 = 9, which is not less than or equal to 4, so it does not satisfy the predicate. For x = 4, we have 4^2 = 16, which is not less than or equal to 4, so it does not satisfy the predicate.

Therefore, the truth set of the predicate is {1, 2}.

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Answer:

17

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer: A( 148 meters )

Answer:

Choice A

Step-by-step explanation:

Using vertical angles, you know the side under the top 20 meters is also 24 meters. Then the most bottom side of the lower garden is 30 meters. You have 30+30+20+20+24+24=2(30)+2(20)+2(24)=2(30+20+24)=2(74)=148. Thus, choice is correct.

DUBS

Please consider giving a brainliest, because you did promise one ;)

Answer:

10 percent

Step-by-step explanation:

7.5 times 10 = 75.

plez give me brainiest

Answer:

d)142º

Step-by-step explanation:

\(\widehat{AB}=2\times71\º=142\º\)

Answer:

Given statement is false.

Step-by-step explanation:

Given that,

All irrational numbers have some repeating pattern which can  be used to compare them to rational numbers.

We know that,

Rational number :

A rational number is defined such a number which can be written as a ratio.

It means we can write a rational number as a fraction.

For example : 2, 3/2 and 4/2... etc.

In the fraction, both number are4 whole number.

So, we can say that, a number which can be define as a fraction it is called rational number.

Irrational number :

An irrational number is defined such a number which can not be written as a ratio.

For example : √5, √10 and √15...etc

So, we can say that, a number which can not be define as a fraction it is called irrational number.

We need to find all irrational numbers have some repeating pattern which can  be used to compare them to rational numbers

According to rational number and irrational number

This statement is false.

Suppose, √2 is irrational but not repeating.

So, we can't write √2 as rational number.

Hence, Given statement is false.

Answer:

Step-by-step explanation:

To have anything to a power is just multiplying the number as many times as it says to.  ex. 2^3 is two times itself 3 times. 2 x 2 x 2= 8

In your case, you need to multiply -4 x -4 because the exponents tell you how many of the number you multiply.

-4 x -4 = 16

Hope this helps :)

Answer:

6x+6 or 4x+10

Step-by-step explanation:

hope u like it

Answer:

a) 196cm^2

b) 225cm^2

c) 180 cm^2

Step-by-step explanation:

a) The figure is a square, so you can use the formula: a = l^2, or area equals length of one side squared.

a = (14cm)^2

a = 196cm^2

b) a = (15cm)^2

   a = 225cm^2

c) This one is a parallelogram, so it's trickier. However, we can imagine the figure as a rectangle by taking the small triangle that sticks out on the right and putting it into the gap in the left. Now, we can solve this using the formula for a rectangle: a = l x w.

a = l x w

a = 18cm x 10 cm = 180 cm^2

:)

Answer:

6.00b + 7.75s ≥ 250

b + s ≤ 40

Step-by-step explanation:

6.00b + 7.75s ≥ 250---this represents how much he will make

b + s ≤ 40---these are his hours. B+S are his hours, and they can't be greater than 40 hrs, so ≤.

The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].

Let's go step by step to find the LU factorization of matrix A.

Matrix A:

A =

[4, -8, 10]

[-8, 8, -7]

[6, -7, 3]

Step 1:

Initialize the L matrix as an identity matrix of the same size as A.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 2:

Perform Gaussian elimination to obtain U.

- Multiply the first row of A by (1/4) and replace the first row of A with the result.

A =

[1, -2, 2.5]

[-8, 8, -7]

[6, -7, 3]

- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[6, -7, 3]

- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Step 3:

Update the L matrix based on the operations performed during Gaussian elimination.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 4:

The resulting matrix A is the upper triangular matrix U.

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Therefore, the LU factorization of matrix A is:

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

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