Find the function y(x) satisfying d^{2}y/dx^2 = 4 -36x, y'(0)=5, and y(0) = 4.

Answer:

The answer to your problem is, 22.3 ft

Step-by-step explanation:

Here we can make a triangle rectangle with the following vertex:

The catheti of this triangle rectangle will be:

! Tan(a) = opposite cathetus/adjacent cathetus. !

Tan(25°) = H/36ft

Solving for H we ge; Tan(25°)*36ft = H = 16.8 ft

The height of the flag pole minus the height of her eye level, then the actual height of the flagpole is:

\(H + 5.5ft = 16.8 ft + 5.5ft = 22.3 ft\)

Thus the answer is, 22.3 ft

The probability of drawing a red 7 and black face card is P ( A ) = 1/221

Given data ,

Let the probability of drawing a red 7 and black face card be P ( A )

Now , the compound probability is given by\

The number of red 7 cards = ( red of diamonds 7 + red of hearts 7 )

Probability of drawing a red 7 = 2/52

Now , the card is not replaced , so the total number of remaining cards = 51

And , number of black face cards = 6

Probability of drawing a black face card = 6/51

So , P ( A ) = 2/52 ( 6/51 )

P ( A ) = 12 / 2652

On simplifying , we get

P ( A ) = 1/221

Hence , the probability is P ( A ) = 1/221

To learn more about probability click :

https://brainly.com/question/17089724

#SPJ1

Answer:

a₉ = 13

Step-by-step explanation:

a₉ = \(S_{9}\) - \(S_{8}\) = 27 - 14 = 13

The particular solution to the differential equation subject to the given initial condition is B(t) = 15e^(-0.3t).

To find the particular solution to the differential equation subject to the given initial condition, dB/dt + 0.3B - 30 = 0 and B(3) = 6, follow these steps:

Step 1: Rewrite the given differential equation as dB/dt = -0.3B + 30.

Step 2: Solve the homogeneous equation dB/dt = -0.3B. This is a first-order linear differential equation, and the solution is B(t) = Ce^(-0.3t), where C is the integration constant.

Step 3: Substitute the initial condition B(3) = 6 into the equation B(t) = Ce^(-0.3t) to find the value of C. So, 6 = Ce^(-0.3(3)).

Step 4: Solve for C. First, find the value of e^(-0.9) ≈ 0.40657. Then, divide both sides of the equation by this value: C ≈ 6 / 0.40657 ≈ 14.75. Round C to the nearest integer, which is 15.

Step 5: Substitute the value of C back into the equation B(t) = Ce^(-0.3t) to find the particular solution: B(t) = 15e^(-0.3t).

So, the particular solution to the differential equation subject to the given initial condition is B(t) = 15e^(-0.3t).

Learn more about differential equations:https://brainly.com/question/28099315

#SPJ11

x=3.07 metre / 3m ( neglecting the decimal)

Answer:x=3.07

Step-by-step explanation:

4 square root 2=(4×2)(2 4-3)÷ 2 square root 2

Answer =3

3.07

The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

To learn more about standard deviation, please check: https://brainly.com/question/26201837

#SPJ1

Step-by-step explanation:

360 divided by 1/12 = 30

360 - 30 = 330

330 divided by 1/6 = 55

330 - 55 = 275

Answer: Abby has 275 pages left to read.

Answer:

This graph shows a function because no vertical line passes through more than one point on the graph.

Step-by-step explanation:

Answer:

18 = 4(3)+6

12 + 6

Step-by-step explanation:

the answer is 18 = 4(3)+6

because y is 18

Answer:

x=3

Step-by-step explanation:

\(18 = 4x + 6\)

subtract 6 on both sides

\(12 = 4x\)

divide both sides by 4

\(3 = x\)

Step-by-step explanation:

y=x+6.......(1)

y=-3X-6....(2)

from eq (1), we get,

x=y-6....(3)

sub eq (3) in eq (2), we get

y= -3(y-6)-6

y= -3y+18-6

y+3y-12=0

4y=12

y=3

sub value of y in eq (3)

x=3-6

x=-3

Answer: (3, 3)

Step-by-step explanation:

There are three general ways of solving a system of equations:

When solving systems of equations with graphing, look for points that overlap with each other or cross, and that will be the solution for the system. There might be one, two, or more than two solutions.

Please refer to the attachment below for the graph of the two equations.

Hope this helps!! :)

Please let me know if you have any questions

The largest area a rectangle can have when inscribed in a semicircle of radius 2 is 4 square units.

The dimensions of this rectangle are 2 units by 2 units. This occurs when the sides of the rectangle are parallel to the diameter of the semicircle, so that each vertex of the rectangle lies on the circumference of the semicircle.

The length of the rectangle is equal to the diameter of the semicircle, or 2 units, and its width is half the diameter, or 2/2 = 1 unit. The area of this rectangle is equal to the length times the width, or 2 * 1 = 2 square units.

Since the rectangle is inscribed in a semicircle, its dimensions must be equal, so the largest area rectangle that can be inscribed in a semicircle of radius 2 has sides of length 2 units and an area of 4 square units.

To know more about area a rectangle click on below link:

https://brainly.com/question/20693059#

#SPJ11

Answer:

x= -3 / 8

Step-by-step explanation:

5x+7+3x-4=0

Sum 5x and 3x

8x+7-4=0

Subtract 7-4

8x+3=0

Move the constant to the other side and change his symbol with his opposite

8x=-3

8 is multiplying x, the opposite of multiplying is dividing, so it divide the -3 (under it)

x= -3 / 8

Answer:

\( \sqrt{ {8}^{2} +{10}^{2} } = \sqrt{64 + 100} = \sqrt{164} =2\sqrt{41}\\ =\boxed{12.8\: units} \)

The diagonal length of the rectangular book is 12.8 units.

A rectangle is "four sided polygon, having all the internal angles  is equal to 90 degree. The two sides of each corner is right angles".

According to the question,

The length of rectangle is 8 units and the breadth of rectangle is 10 cm.

To find diagonal of the rectangle: Using Pythagoras theorem a² + b² = c².

c = \(\sqrt{a^2 + b^2}\)

  = \(\sqrt{8^2 + 10^2}\)

  = \(\sqrt{64 + 100}\)

  = \(\sqrt{164}\)

  = 2\(\sqrt{41}\)

  = 12.8 units

Hence, the diagonal length of the rectangular book is 12.8 units.

Learn more about rectangle here

https://brainly.com/question/17043608

#SPJ2

Answer and Step-by-step explanation:

To find the length of AB, we have to use Distance Formula.

Distance Formula takes two points on a graph, and puts it into the following formula to calculate the distance between those two points.

The formula:

D = \(\sqrt{(x_{2} - x_1)^2 + (y_2 - y_1)^2 }\)

Where:

D = The Distance between two points

\(x_2\) = The x value of the second point

\(x_{1}\) = The x value of the first point

\(y_2\) = The x value of the second point

\(y_{1}\) = The x value of the first point

Point A will be the first point and point B will be the second point. All we have to do now is plug those points into the formula and solve.

\(\sqrt{(10 - 5)^2 + (0 - 10)^2 }\\\\\\\\\sqrt{(5)^2 + (- 10)^2 }\\\\\\\\\sqrt{25 + 100 }\\\\\\\\\sqrt{125}\\\\\\\\\sqrt{125} = 5\sqrt{5}\)

The length of side AB is \(5\sqrt{5}\) units, or 11.18 units.

I hope this helps!

#teamtrees #PAW (Plant And Water)

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Check the picture below.

Answer:the answer would be 4

Step-by-step explanation: you multiplied the 1 by 2, 2 by 4, 3 by 6.

The appropriate answer is B: There's not enough evidence to decide whether the distribution is skewed or roughly symmetric.

a. The quartiles divide the data into four equal parts. Q1 (the first quartile) is the median of the lower half of the data, Q3 (the third quartile) is the median of the upper half of the data. In this case, Q1 is 71 pounds, which means that 25% of the high school female athletes had a maximum bench press less than or equal to 71 pounds. Q3 is 91 pounds, indicating that 75% of the athletes had a maximum bench press less than or equal to 91 pounds.

b. Based on the given information, we can make an educated guess about the distribution's symmetry. The median (81 pounds) is equal to the mean, which suggests a roughly symmetric distribution. Additionally, the values of Q1 (71 pounds) and Q3 (91 pounds) are symmetrically distributed around the median. However, without additional information or a graphical representation of the data, we cannot definitively determine the distribution's skewness.

For more such questions on symmetric

https://brainly.com/question/30031806

#SPJ8

Given that John surfs the website on a regular basis. The time he spent surfing the website per day is normally distributed, µ = 8 minutes and σ = 2 minutes. If you select a random sample of 4 sessions. We are to find the probability of sample mean.a.

The probability that the sample mean is less than 8 minutes sample size(n) = 4μ = 8 minutesσ = 2 minutes

As we know, the sample means follow a normal distribution with mean, μ and standard deviation, σ / sqrt(n).

Therefore, the sample mean will follow a normal distribution with a mean of μ and standard deviation of σ/√n=2/√4=1

So the Z-score for the given data can be calculated as: Z= X−μ/σ/√nZ= 8−8/2/√4=0Thus, the probability that the sample mean is less than 8 minutes is P(Z < 0).

Since the Z distribution is normal, the area to the left of 0 is 0.5.

Therefore, the probability that the sample mean is less than 8 minutes is 0.5.b. The probability that the sample mean is between 8 and 10 minutes sample size(n) = 4μ = 8 minutesσ = 2 minutes

The Z-scores corresponding to X1=8 and X2=10 can be calculated as: Z1= X1−μ/σ/√n= 8−8/2/√4=0Z2= X2−μ/σ/√n= 10−8/2/√4=1

Thus, the probability that the sample mean is between 8 and 10 minutes is the area under the standard normal curve between Z1 and Z2, which is P(0

To know more about probability visit:

https://brainly.in/question/996463

#SPJ11

Answer:

\(-45n+55\)

Step-by-step explanation:

The expression 10 - 5(9n - 9) in the simplified form will be 55 - 45n.

Given that:

Expression, 10 - 5(9n - 9)

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Simplify the expression, then we have

⇒ 10 - 5(9n - 9)

⇒ 10 - 45n + 45

⇒ 55 - 45n

More about the simplification link is given below.

https://brainly.com/question/12616840

#SPJ6

Answer:

Step-by-step explanation:

To calculate the walking rate, you have to think of the unit that the walking rate is in. Walking rate is most often in meters per second or kilometres per hour, so I'll explain both. The first one (m/s) is easy, since both are already in these units. The formula speed = distance/time can be used here, which gives 12/3 = 4 meters per second.

For km/h it is a little more difficult. 12 meters equals 12/1000 kilometers (which is 0.012), since there are 1000 meters in a kilometer. Then 3 seconds equals 3/60 minutes (which is 0.05 mins), which is 0.05/60 hours (which is 0.0083333). Using the formula now, the answer is 0.012/0.0083333 = 14/4 km/h

The remainder when the sum of all three-digit positive integers with three distinct digits is divided by 10001000 is 549,450

To find the sum of all three-digit positive integers with three distinct digits, we can use the concept of arithmetic progression.

An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. In this case, the difference between consecutive three-digit positive integers is 1.

To find the sum of an arithmetic progression, we can use the formula: Sum = (first term + last term) * number of terms / 2

In this case, the first term is 100, the last term is 999 (the largest three-digit positive integer with three distinct digits), and the number of terms is the count of numbers between 100 and 999 inclusive.

To find the count of numbers between 100 and 999 inclusive, we subtract the starting number from the ending number and add 1:

(999 - 100) + 1 = 900.

Substituting the values into the formula, we get:

Sum = (100 + 999) * 900 / 2 = 549,450

Now, to find the remainder when the sum is divided by 10001000, we can use the modulo operation.

Remainder = 549,450 % 10001000

= 549,450

Therefore, the remainder when the sum is divided by 10001000 is 549,450.

The remainder is 549,450.

To find the sum of all three-digit positive integers with three distinct digits, we can use the concept of arithmetic progression.

The first term is 100, the last term is 999, and the difference between consecutive terms is 1.

The formula for the sum of an arithmetic progression is

(first term + last term) * number of terms / 2.

In this case, the number of terms is the count of numbers between 100 and 999 inclusive, which is

(999 - 100) + 1 = 900.

Substituting the values into the formula, we get a sum of 549,450. To find the remainder when the sum is divided by 10001000, we can use the modulo operation.

The remainder is 549,450.

The remainder when the sum of all three-digit positive integers with three distinct digits is divided by 10001000 is 549,450.

To Know More about formula visit:

brainly.com/question/20748250  

#SPJ11

Answer:

The error in his prediction is that he had too small of a sample size for the data to be reliable in how the trend would continue.

Answer:

He did not perform enough trials to compare the theoretical and experimental probabilities.

Step-by-step explanation:

Answer:

90$

Step-by-step explanation:

We need to find 15% of the number 600:

\( \frac{600 \times 15\%}{100\%} = 90 \)

So, the answer is 90$

Answer:

C. y = x + 2

Step-by-step explanation:

2 is being added onto both sides

The correct response is D. a segment of a line that goes on forever in one direction from one terminal.

A line is a one-dimensional, perfectly straight shape that extends forever and is infinitely thin in both directions. A line may be referred to as a straight line or, more formally, a right line (Casey 1893), to stress that there are no "wiggles" throughout its entire length. When two points are connected with the smallest possible distance between them and both ends stretched to infinity, a line is the shape that results. Despite the fact that lines don't have a clear beginning or finish, they are represented in our daily lives by things like railroad tracks and freeways. Any section of a line with two fixed endpoints is referred to as a line. Line segments make up a line.

To know more about line here

https://brainly.com/question/13763238

#SPJ4

Answer:

3y

Step-by-step explanation:

Sqrt of 9 = ±3

-±3\(\sqrt{y^{2} }\)

the square and sqrt cancel leaving you with -±3y

Since y < 0, the sqrt of 9 should be -3 to cancel out the - sign in front.

Hope that helps

Answer:

3330.08 inches of 277.51 feet

Step-by-step explanation:

13.25X2X3.14159=length of one rotation=83.25

40 rotations=40(83.25)=3330.08 inches