Dr. Orchid has 9 paintings she wants to hang side by side on her walls.
a) in how many ways can she arrange all 9 paintings?
b) if she wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display?

Answer:

Because she found it improves division.

Step-by-step explanation:

The expected number of full days hereafter that the machine will remain operational before the next breakdown is still 10 days

We calculated that the expected number of full days until the next breakdown was 10 days. Now, suppose that the machine has already gone 15 full days without a breakdown since the last repair was completed. This means that the machine has already exceeded the expected number of full days until the next breakdown.

However, the fact that the machine has already gone 15 full days without a breakdown does not change the underlying probability distribution of the time until the next breakdown. The distribution is still exponential with a mean of 10 days. Therefore, even though the machine has already exceeded the expected number of full days until the next breakdown, the expected number of full days hereafter that the machine will remain operational before the next breakdown is still the same as before: 10 days.

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In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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The question given is incomplete. Completed question is given below the answer.

The set,  {(x, y)|9<x2+y2<25} is open and connected.

The following set, {(x, y)|9<x2+y2<25} is:

A. is open (all points of the set are interior)

B. is connected (since it can not be divided into parts)

C. it is not simply connected (it has holes)

D. False, according to the previous answers

Open Set:

In mathematical terms, a set is said to be open if all its points are interior.

That is to say, no point that belongs to the border of the set or is isolated belongs to the set.

Determine the qualities of the given set. (Select all that apply.)

{(x, y)|9<x2+y2<25}

A. open

B. connected

C. simply connected

D. none of the above

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Answer:

111001010001010000101001011101000000011010101110010010010101010010

Step-by-step explanation:

Answer:

13 + \(\sqrt{89}\)

or

22.43398... (depends on how you round it)

Step-by-step explanation:

1. The question stated that the radius of the circle O is 5, so the length of AO and CO is 5.

2. Since line AB and line CB are both tangent to the circle, they have the same length. CB is 8, so AB will also be 8.

--> Both triangle AOB and COB share one side, and the other side (radius) has the same length, so the third side must be the same length

3. Tangent means having a 90-degree angle with the radius. We know that the triangle AOB is a right triangle since the angle OAB is 90 degrees.

We can use the Pythagorean theorem to find side OB. OB^2 = AO^2 + AB^2.

--> OB^2 = 25 + 64

--> OB^2 = 89

--> OB = \(\sqrt{89}\)

Now that we know the lengths of all three sides, we can add them up.

--> 5 + 8 + \(\sqrt{89}\)

--> 13 + \(\sqrt{89}\)

or

--> 22.43398113....

Therefore, the length of the curve is 10√(34).

We need to find the length of the curve given by r(t) = 5t, 3 cos(t), 3 sin(t) on the interval -5 ≤ t ≤ 5.

The length of the curve is given by the formula:

L = ∫_a^b ||r'(t)|| dt

where ||r'(t)|| represents the magnitude of the derivative of the vector function r(t).

First, we find the derivative of r(t):

r'(t) = 5, -3 sin(t), 3 cos(t)

Then, we find the magnitude of r'(t):

||r'(t)|| = √(5^2 + (-3 sin(t))^2 + (3 cos(t))^2)

= √(25 + 9 sin^2(t) + 9 cos^2(t))

= √(34)

Thus, the length of the curve is:

L = ∫_{-5}^5 ||r'(t)|| dt

= ∫_{-5}^5 √(34) dt

= √(34) [t]_{-5}^5

= √(34) (5 - (-5))

= 10√(34)

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The required, there are 8998912 possible license plates that can be generated using this format.

Here, we have,

There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.

Therefore, there are 8 choices for each of the three digits,

giving us 8 x 8 x 8 = 512 possible combinations for the digits.

Similarly, there are 26 letters that can be used for each of the three letters on the license plate.

Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.

Total number of license plates = number of choices for the digits x number of choices for the letters

= 512 x 17576

= 8998912

Therefore, there are 8998912 possible license plates that can be generated using this format.

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Answer:

49degrees

Step-by-step explanation:

The sum of angle on a straight line is 180degrees, hence;

x + y + z = 180

x + 45 + 86 = 180

x + 131 = 180

x = 180 - 131

x = 49degrees

Hence the value of x is 49degrees

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

it would for sure be a

Step-by-step explanation:

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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well, the volume of that triangular prism will just be the area of the triangle times the length.

now, what's the area of that triangular face?  well, let's say it has a base of "b" and a height of 3, whilst the prism has a length of 6, Check the picture below.

\(\stackrel{\textit{triangle's area}}{\cfrac{1}{2}(b)(3)}\stackrel{\textit{prism's length}}{(6)}~~ = ~~4\frac{1}{2}\implies 9b=\cfrac{9}{2}\implies b=\cfrac{9}{18}\implies b=\cfrac{1}{2}\)

Answer: 17/2

Step-by-step explanation:

\(f(9)=9-\frac{1}{2}=\frac{17}{2}\)

The required equation of line v perpendicular to line u is given as y = -x - 9

Given that,
Line u has an equation of y=-x+7. line v is perpendicular to line u and passes through (-8,-1).

The line is a curve showing the shortest distance between 2 points.

here,
The slope of the line perpendicular to the other is given as the negative reciprocal of the slope of another line,
So,
The slope of line v = - 1/ slope of the line u
m = -1/1
m = -1
Now,
Line v is passing by points [-8, -1],
Equation of the line v is given as,
y + 8 = -1 [x + 1]
y = -x - 1 - 8
y = -x -9

Thus, the required equation of line v perpendicular to line u is given as y = -x -9.

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The wavelength of the photon emitted when a hydrogen electron transitions from the n=3 to the n=2 energy level is approximately -7.854 x 10⁻⁸ meters..

The wavelength of the photon emitted when a hydrogen electron transitions from the n=3 to the n=2 energy level can be calculated using the Rydberg formula.

The Rydberg formula is given by:

1/λ = R(1/n₁² - 1/n₂²)

Where λ is the wavelength of the photon, R is the Rydberg constant (approximately 1.097 x 10⁷ m⁻¹), n₁ is the initial energy level, and n₂ is the final energy level.

In this case, the initial energy level (n₁) is 3 and the final energy level (n₂) is 2.

Plugging these values into the formula, we get:

1/λ = R(1/3² - 1/2²)

Simplifying further:

1/λ = R(1/9 - 1/4)

1/λ = R(4/36 - 9/36)

1/λ = R(-5/36)

To find the value of λ, we take the reciprocal of both sides:

λ = -36/5R

Substituting the value of R (1.097 x 10⁷ m⁻¹), we get:

λ ≈ -36/5(1.097 x 10⁷ m⁻¹)

Calculating this value, we find:

λ ≈ -7.854 x 10⁻⁸ m.

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The wavelength of the photon emitted when a hydrogen electron transitions from the n1 to the n2 energy level can be calculated using the Rydberg formula: 1/λ = R((1/n1^2) - (1/n2^2)), where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.

When a hydrogen electron transitions from one energy level to another, it emits or absorbs a photon of specific energy. This energy can be related to the wavelength of the photon using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

In the case of a hydrogen atom, the energy levels are quantized and given by the equation E = -13.6 eV/n^2, where n is the principal quantum number. The initial energy level, n1, is usually a higher value than the final energy level, n2.

Using the Rydberg formula, we can determine the wavelength of the emitted photon. By substituting the values of n1 and n2 into the equation, we can calculate the wavelength.

For example, if the electron transitions from n=3 to n=2, the Rydberg formula becomes 1/λ = R((1/3^2) - (1/2^2)). Solving for λ will give us the wavelength of the emitted photon.

Please note that the Rydberg formula is specifically applicable to hydrogen atoms or hydrogen-like ions.

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Answer:

44ft

Step-by-step explanation:

12ftx6ft=72ft

72ftx2ft= 144ft

144ft-100ft=44ft

Hope this helps! :)

95% confidence interval for the mean sales price of all houses in the community is $273,106 to $296,894 which is the lower limit and upper limit respectively.

a) The lower limit of the 95% confidence interval can be found using the formula:

Lower limit = sample mean - (z-value) x (standard error)

where the z-value for a 95% confidence interval is 1.96, and the standard error is the standard deviation divided by the square root of the sample size:

Standard error = standard deviation / sqrt(sample size)

Substituting the given values, we get:

Standard error = 13000 / √(10) = 4119.9

Lower limit = 285000 - (1.96 x 4119.9) = $275,094.26

Therefore, the lower limit of the confidence interval is $275,094.26.

b) The upper limit of the 95% confidence interval can be found using the same formula, but with a positive value of the z-value:

Upper limit = sample mean + (z-value) x (standard error)

Substituting the given values, we get:

Upper limit = 285000 + (1.96 x 4119.9) = $294,905.74

Therefore, the upper limit of the confidence interval is $294,905.74.

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The question is -

Suppose that a random sample of ten recently sold houses in a certain city has a mean sales price of $285,000, with a standard deviation of $13,000. Under the assumption that house prices are normally distributed, find a 95% confidence interval for the mean sales price of all houses in this community.

a) What is the lower limit of the confidence interval?

b) What is the upper limit of the confidence interval?

Answer:

942m^3

Step-by-step explanation:

Given data

Radius of cone= 5m

Height= 12 m

We know that volume of a cone is given as

V= πr^2h

V= 3.14*5^2*12

V= 3.14*25*12

V= 942 m^3

Hence the volume is 942m^3

Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.

As given in the question,

Perimeter of the rectangular area encloses for fencing = 3200 yards

Let 'x' and 'y' be the length and width of the rectangle.

2( x + y ) = 3200

⇒ x + y = 3200/2

⇒y = 1600 - x

Area of rectangular field 'A' = xy

⇒ A = x ( 1600 - x )

⇒ A = 1600x - x²

Differentiate both the side of the equation we get,

dA/dx = 1600 - 2x

For Maximum Area dA/dx = 0

1600 -2x =0

⇒ 2x = 1600

⇒ x= 800 yards

Now, y = 1600 - 800

          = 800 yards

Maximum area = (800) (800)

                        = 640,000 square yards

Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.

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The equation of the line is y = 4x. Option B

First, we need to know that the general equation of a line is expressed as;

y = mx + c

Such that the parameters of the formula are expressed as;

From the information given, we have that the points in the line are;

(1,-4)

(2,-8)

Now, let us determine the slope of the line, we have to take the change in the value of the points

Slope, m = -8 -(-4)/2-1

expand the bracket

Slope, m = 4

Then, the intercept is;

-8 = 4(2) + c

c = 0

Equation of the line would be;

y = 4x

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Answer:

0.5857 radian

Step-by-step explanation:

Given :

Length of fence = 6 feets

Height of fence from ground after tilt = 5 feets

The tilt angle is represented by θ ;

To obtain the angle ; we use the trigonometric relation :

Cosθ = adjacent / hypotenus

Cos θ = 5 / 6

θ = Cos^-1(5/6)

θ = 33.557°

Converting to radian :

33.557 * π/180

= 33.557 * 0.0174532

= 0.58568

= 0.5857 radian

Answer:

6p = 42

Step-by-step explanation:

If everybody scores 6 then the possible equation could be 6p = 42.

p represents the people on the team.

Solve for the variable p:

6p = 42

6p/6 = 42/6

p = 7

There are 7 people on the team.

hope this helps and is right!! p.s. i really need brainliest :)

Use the point to find the value of either a or p depending on the orientation of the parabola. Substitute the values of h, k, and a or p into the standard form equation of a parabola to get the equation of the parabola in standard form.

The main answer is:Assuming that the orientation of the parabola is upward, the equation of the parabola in standard form is (y - k) = a(x - h)². Given the vertex and a point on a parabola, the coordinates of the vertex are (h, k). Let the point on the parabola be (x₁, y₁).We have h, k, x₁, and y₁. Our next step is to find the value of a using the point (x₁, y₁). Since the orientation of the parabola is upward, the value of a is positive.

This distance is also equal to the distance between (x₁, y₁) and the directrix. Hence,d = |y₁ - p|, where p is the distance between the vertex and the directrix.Since the vertex is the midpoint between the focus and the directrix, then the distance between the vertex and the focus is also p. Therefore, 4p = |y₁ - k|². This is because the distance between the vertex and the focus is equal to four times the distance between the vertex and the directrix.

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⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

10

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

Step-by-step explanation:

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

First let know what we are doing..

Given:

A bouquet has 30 flowers

Size of bouquet decrease by a factor of 3

How many flowers remains

Note;

The term "decreased by a factor" means to divide.

Solve;

Thus, 30/3 = 10

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

[RevyBreeze]

The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Generally, the equation for three points is mathematically given as

a+2b+4c=1.....1  for the variable (1, 2)

4a+4b+4c=1.....2  for the variable (2, 2)

9a+3b+c=1.....3  for the variable (3, 1)

Step 1

Here we solve equations 1 and 2 simultaneously to find the value of b

Therefore

equ 2-equ1

3a+2b=0

b=-1.5a....4

Step 2

We solve equations 1 and 3 simultaneously to find the value of c

Where

9*equ1-equ3 gives

-15b-35c=-8

c=8-15b

subbing equ 4 we have

c=8+22.5a ....5

Step 3

Put values of b and c in equation 2, and we have

4a-6a+32+90a=1

a=-31/88

a=-0.3523

The value of b will be

b=-1.5*a

b=0.5284

The value of b will be

c=8-22.5*a

c=15.9268

Step 4

In conclusion, the equation is given as

By substituting the values of a b and c into the general formula we have

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

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The appropriate hypotheses

Н0 = μ = 23.9

HA = μ > 23.9

The first step in hypothesis testing is to state the null hypothesis (H0) and the alternative hypothesis (HA). In this case, the null hypothesis is that the mean age at which men first marry has not changed since 1960. The alternative hypothesis is that the mean age at which men first marry has increased since 1960.

H0 = μ = 23.9

HA = μ > 23.9

If the sample mean age is significantly greater than 23.9 years, we would reject the null hypothesis and conclude that there has been an increase in the mean age at which men first marry in the region since 1960.

If the sample mean age is not significantly greater than 23.9 years, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean age at which men first marry has increased since 1960.

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The area of the triangle is 31.54 square units

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

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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