Please provide answers symbolically
(a) Solve the initial value problem (x - 1)y' - x264 y = 5(x – 1), 5(x - 1)2, H2) = 0 = (b) Write the largest interval (a, b) of x on which the solution is defined. If either a or b is infinite, type either infinity, or infinity.
Enter the values of a and b (in that order) into the answer box below, separated eith a commma.

The 95% confidence interval for the given population proportion is between 0.1716 to 0.2884.

The confidence interval for a population proportion is calculated by the formula,

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

Where \(\bar{p}\) is the sample proportion and α is the level of significance.

It is given that,

The statistics reported on CNBC projects, a surprising number of motor vehicles are not covered by insurance. The sample results are

The sample size n = 200;

The number of successes = 46

So, the sample proportion \(\bar{p}\) = 46/200 = 0.23

For a 95% confidence interval, the level of significance is

α = 1 - 95/100 = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Then, the z-score for the value 0.025 is

\(z_{\alpha/2}\) = 1.96 (from the table)

Thus, the confidence interval is

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

⇒ C.I = 0.23 ± (1.96) × \(\sqrt{\frac{0.23(1-0.23)}{200} }\)

⇒ C.I = 0.23 ± 1.96 × 0.0298

⇒ C.I = 0.23 ± 0.0584

So, the upper limit is 0.23 + 0.0584 = 0.2884 and the lower limit is 0.23 - 0.0584 = 0.1716.

Therefore, the 95% confidence interval for the given population proportion lies between 0.1716 to 0.2884.

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Answer:

Step-by-step explanation:

A number less than 3 is 2 or 1 which is 2/6 of the time

A coin can land on either side with a probability of 1/2

P(h and <3) = 1/2 * 2/6 = 1/6

This is exactly what you got.

Step-by-step explanation:

The amplitude is the value that the cosine is being multiplied by.

The general equation of a sinusoid is

\( a \cos(b(x + c) ) + d\)

where a is the amplitude

\( \frac{2\pi}{ |b| } \)

is the period

-c is the phase shift

d is the midline(vertical shift)

Here the amplitude is -1/2 so b is the correct answer.

Answer:

the amplitude of the function that is y= -1/2 cos x, is 1/2.

Step-by-step explanation:

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

  an = 5/2 +3/2(n -1)

Step-by-step explanation:

The common difference is ...

  4 -5/2 = 3/2

The general rule is ...

  an = a1 +d(n -1)

For a1 = 5/2 and d = 3/2, the rule for this sequence is ...

  an = 5/2 +3/2(n -1)

___

This can be simplified to ...

  an = 1 +3/2n

Answer:

x=136°

Step-by-step explanation:

x=136° ( as it's vertical angle to 136°)

The nature of formula (Permutations or Combinations) for each scenario is the following:

1) Permutations ; 2) Combination

3) Combination ; 4) Permutations

5)Permutations ; 6)Combination

7) Combination ; 8)Combination 9)Combination ; 10)Combination.

Permutations formula: Permutation is considered an ordered combination. The general formula for this is,

P(n, r) = n! /(n-r)!

Combination formula: It is considered arrangement ways but without ordered combination. The general formula for this is C(n, r) = n!/ (n-r)! r!

Now, we have provide some situations and we have to resolve them.

1) Determining the top three winners ing Science Quiz have to Bee is an example of Permutation as here we just arrange the position for top winners.

2) Forming lines from six given points with no three of which are collinear, is an example of combination because only pair of points is needed.

3) It will be a combination as here we select 3 points to make a triangle user.

4) Four people posing for pictures is an example of Permutation as oder does not matter.

5) Assembling a jigsaw puzzle is an example of Permutations.

6) As here we choose 2 household chores so it is a combination.

7) Selecting 5 basketball players out of 10 team members for the different positions members it is a combination.

8) Choosing three friend for birthday party is combination formula.

9) Picking 6 balls from a basket by 12 balls is combination formula.

10) Forming a committe of 5 members from do people 20 combinations people.

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Complete question:

P- Permutations or C- Combinations.

1. Determining the top three winners in a Science Quiz Bee

2. Forming lines from six given points with no three of which are collinear

3. Forming triangles from 7 given points with no three of which are collinear

4. Four people posing for pictures

5. Assembling a jigsaw puzzle

6. Choosing 2 household chores to do before dinner

7. Selecting 5 basketball players out of 10 team members for the different positions

8. Choosing three of your classmates to attend your party

9. Picking 6 balls from a basket of 12 balls

10. Forming a committee of 5 members from 20 people

The approximate root mean square velocity of neon is similar to that of krypton at the same temperature.

The approximate root mean square (RMS) velocity of a gas is directly proportional to the square root of its temperature, according to the kinetic theory of gases. Since both neon and krypton are noble gases and have similar properties, we can assume that at the same temperature, their RMS velocities will be approximately equal.

Therefore, the approximate RMS velocity of neon would be similar to that of krypton when both gases are at the same temperature. This means that, on average, the individual gas particles in both neon and krypton would have similar speeds or velocities.

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The root mean square velocity of a gas at a given temperature is inversely proportional to its molecular mass. Hence, at the same temperature, Neon, having a lower molecular mass than Krypton, will have a greater root mean square velocity.

The root mean square velocity (rms) of a gas can be determined by the equation Vrms = sqrt(3kT/m), where k is Boltzmann's constant, T is the temperature, and m is the molecular mass. Given that the temperature and Boltzmann's constant remain the same for both neon and Krypton, the factor that influences the velocity is the molecular mass. The lower the molecular mass (m), the higher the velocity. Neon has a lower molecular mass than Krypton, so at the same temperature, Neon's approximate root mean square velocity will be greater than that of Krypton.

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68% of the population will have a height within the range of 69 inches to 75 inches. None of the provided options match this range.

In a normal distribution, approximately 68% of the values fall within one standard deviation of the mean.

Given:

mean height = 72 inches  

standard deviation = 3 inches,

We can determine the range within which 68% of the population's heights will fall.

To calculate this range, we subtract and add one standard deviation from the mean:

Lower bound: Mean - Standard Deviation

= 72 - 3

= 69 inches

Upper bound: Mean + Standard Deviation

= 72 + 3

= 75 inches

Therefore, 68% of the population will have a height within the range of 69 inches to 75 inches.

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Step-by-step explanation:

if the green marble is probably rare the red marble should have a probability of 1/45

i hope you like it.

Answer: x=9

Step-by-step explanation: 2(x+5+)=3x+1 or 2x+10=3x+1

Answer:

x =  9

Step-by-step explanation:

2(x + 5) = 3x + 1  Distribute the 2

2x + 10 = 3x + 1  Subtract 2x from both sides

10 = x + 1  Subtract from both sides

9 = x

Check:

2(x + 5) = 3x + 1

2(9 + 5) = 3(9)+1

2(14) = 27 + 1

28 = 28

Answer:

Step-by-step explanation:

6th term.

a

6

=

32

7th term.

a

7

=

36

Answer:B.5√13 cm

Step-by-step explanation: Using Pythagoras' theorem that states -

\(Hypotenuse^{2}\) = \(base^{2}\)+\(perpendicular^{2}\)

Here,

Hypotenuse = x , say

Base = 10 cm

Perpendicular = 15 cm

\(x^{2}\)=\((10)^{2}\)+\((15)^{2}\)

⇒ \(x^{2}\) = 100+225

⇒ x = \(\sqrt{325}\) = 5\(\sqrt{13}\) cm

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Answer:

14+9 14×9that is the answer

Answer:

The paint mixer should use 3 1/3 gallons of 15% gloss paint and 1 2/3 gallons of 30% gloss paint.

Step-by-step explanation:

To make a paint of 20% gallon, the quantity of gloss in 5 gallons of 20% gloss.

0.2 × 5 = 1 gallon.

To get 1 gallon from a combination of 15% gallon and 30% gallon.

Let x rep the volume of 15% gallon.

The volume of 30% gallon can be given as;

5-x.

And we can interpret to form the equation below.

0.15x + 0.3(5-x) = 1

0.15x+1.5-0.3x = 1

-0.15x = 1-1.5 = -0.5

x = -0.5/-0.15

x = 10/3 = 3 1/3

5-x = 5-10/3 = 5/3 = 1 2/3

Therefore, the gallons of 15% = 3 1/3

And the gallons of 30% = 1 2/3

Answer:

......

Step-by-step explanation:............

The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:

x = 2 and y = 0

Step-by-step explanation:

Let's solve your system by elimination.

2x−3y=4;4x+3y=8

2x−3y=4

4x+3y=8

Add these equations to eliminate y:

6x=12

Then solve 6x=12 for x:

6x=12

x = 2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x−3y=4

Substitute 2 for x in 2x−3y=4:

(2)(2)−3y=4

−3y+4=4  (Simplify both sides of the equation)

−3y+4+−4=4+−4  (Add -4 to both sides)

−3y=0

y = 0

Answer:

Equal volumes

Step-by-step explanation:

Given

\(h \to\) height of cone

\(d \to\) diameter of cone

\(H \to\) height of cylinder

\(D \to\) diameter of cylinder

Such that:

\(d = 2D\)

\(h =\frac{3}{4}H\)

Required

The relationship between the volumes

The volume of a cylinder is:

\(V_1 = \pi R^2H\)

Where

\(R = 0.5D\)

So:

\(V_1 = \pi (0.5D)^2H\)

\(V_1 = \pi *0.25*D^2H\)

\(V_1 = 0.25\pi D^2H\)

The volume of the cone is:

\(V_2 = \frac{1}{3}\pi r^2h\)

Where

\(r =0.5d\)

\(r = 0.5 * 2D\)

\(r = D\)

and

\(h =\frac{3}{4}H\)

So, we have:

\(V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H\)

\(V_2 = \frac{1}{4}\pi * D^2H\)

\(V_2 = 0.25\pi * D^2H\)

\(V_2 = 0.25\pi D^2H\)

So, we have:

\(V_1 = 0.25\pi D^2H\)

\(V_2 = 0.25\pi * D^2H\)

\(V_1 = V_2\)

Answer: : When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Step-by-step explanation:

Answer:

y = x - 3

Step-by-step explanation:

First, you need to find the slope from the two given points.

y2 - y1 / x2 - x1

= 3 - (-1) / 6 - 2

= 1

The slope is 1x or simply x.

For the y-intercept, you need to plug one of the coordinates into the equation, which is y = x + b

3 = 6 + b

-3 = b

So the equation is y = x - 3

Answer:

i think this is the answer

Answer:

the answer is \(\frac{3}{2}\) or 1.5 or 1\(\frac{1}{2}\)

Step-by-step explanation:

Answer:

Using the ordered pairs (-2, 4) and m= -3 provide the following information: Point - Slope form: or Slope Intercept form : Standard forma

X intercept: Y interce

Step-by-step explanation:

Answer:

m = 0.0125

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

20 percent of 80 is 16, and added to 80 would equal 96

Answer:  

y = 3x

y = 2.2x

y=1/2x

Step-by-step explanation:

i did the test thank me later

The distance from the flagpole to the tree is approximately 27 feet.

To find the distance from the flagpole to the tree, we can use similar triangles and proportions. Let's assume that the distance from the flagpole to the tree is represented by "x."

From the information given, we know that the height of the flagpole is 16 feet and the height of the tree is 40 feet. The shadows cast by these objects meet at the bench, which is 18 feet from the flagpole.

Using the concept of similar triangles, we can set up the following proportion:

(height of flagpole) / (length of flagpole's shadow) = (height of tree) / (length of tree's shadow)

In this case, the height of the flagpole's shadow is 18 feet since it reaches the bench. The length of the tree's shadow is the sum of the length of the flagpole's shadow (18 feet) and the distance from the flagpole to the tree (x).

So we have:

16 / 18 = 40 / (18 + x)

To solve for x, we can cross-multiply and solve the resulting equation:

16(18 + x) = 40 ×18

288 + 16x = 720

16x = 720 - 288

16x = 432

x = 432 / 16

x ≈ 27

Therefore, the distance from the flagpole to the tree is approximately 27 feet.

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Answer:

Step-by-step explanation:

a^6 = a * a * a * a * a * a You can break this into groups of 2 and groups of three.

Groups of 3

a^6 = a * a * a * a * a * a

what that means is that you have 2 groups of 3 which can be written as (a^3)^2 which means that this number is a perfect square.

Groups of 2

a^6 = a * a * a * a * a * a

What this means is that you have (a^2)^3 which is three groups of 2 members. The answer is that you have a perfect cube each member of which is a^2

Answer:

The bearing of A from B is 122°

Answer:

L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Step-by-step explanation:

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 225 sq.ft. Therefore, we have:

L x W = 225

The perimeter of the rectangle is given by:

2L + 2W

We need to find the dimensions of the rectangle that will give the smallest possible perimeter. To do this, we need to minimize the expression for the perimeter subject to the constraint that the area is 225 sq.ft. We can use the method of Lagrange multipliers to solve this problem.

Let f(L, W) = 2L + 2W be the expression for the perimeter and g(L, W) = L x W - 225 be the expression for the area. We want to minimize f(L, W) subject to the constraint g(L, W) = 0.

The Lagrange function is given by:

L(L, W, λ) = f(L, W) - λg(L, W)

= 2L + 2W - λ(LW - 225)

Taking partial derivatives and setting them equal to zero, we get:

∂L/∂λ = W = 0

∂W/∂λ = L = 0

∂L/∂λ = -λW = 0

∂W/∂λ = -λL = 0

∂L/∂λ = 2 - Wλ = 0

∂W/∂λ = 2 - Lλ = 0

Solving these equations, we get:

λ = 2/L = 2/W

Substituting λ in the expression for the area, we get:

L^2 = 225

Therefore, L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Answer:

width = 15 ft

length = 15 ft

Step-by-step explanation:

Let x = length and y = width.

area = length × width

A = xy

perimeter = 2(length + width)

P = 2(x + y)

P = 2x + 2y

A = 225

xy = 225

y = 225/x

P = 2x + 2(225/y)

P = 2x + 450/x

P = 2x + 450x^-1

dP/dx = 2 + 450(-1)(x^-2)

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2x² - 450 = 0

x² - 225 = 0

x = ±√225

x = ±15

Discard x = -15.

width = 15 ft

length = 15 ft