find the area of the regular pentagon

The expected number of rolls until all faces have appeared in some order in six consecutive rolls is 1 / [1 - (5/6)^6].

To find the probability that all faces have appeared in some order in six consecutive rolls of a 6-sided die, we can use the principle of inclusion-exclusion.

Let's calculate the probability of the complement event first, which is the probability that at least one face is missing from the sequence in six consecutive rolls.

In the first roll, there are 6 possibilities for the face that appears. In the second roll, there are 5 possibilities remaining, and so on. Therefore, the probability of missing a face in one roll is (5/6).

Since we want to find the probability of missing a face in six consecutive rolls, we multiply the probabilities together: (5/6)^6.

Now, to find the probability of all faces appearing in some order in six consecutive rolls, we can subtract the probability of the complement event from 1.

Probability = 1 - (5/6)^6.

For the expected number of rolls until such a sequence appears, we can use the concept of geometric distribution. The expected number of rolls for a geometric distribution is equal to 1 divided by the probability of success.

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the average speed of the current in this section of the mississippi river is 5.8

let C = the speed of the current

then B - C = effective speed up river

B+C =effective speed down river

time up + time down = 16.5 hrs

60/B-C+60/B+C= 16.5

taking lcm and solving we get

480+60C +480-60C= 16.5 (64 - C^2)

960= 1056 - 16.5 C^2

16.5 C^2 =96

C^2= 5.82

Hence , the average speed of the current in this section of the mississippi river is 5.8

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The total cost to get 4 orders of fries and 3 drinks is $7.05

The total cost to get ff orders of fries and dd is ($0.93*ff+$1.11*dd)

What is an algebraic expression?

An algebraic expression an expression which is made up of variables and constants, along with algebraic operations such as subtraction, addition, multiplication and division.

In this case, the total cost of fries is cost per fries, which is $0.93 multiplied by the number of fries, ff.

The total cost drinks is the cost per drink which is $1.11 multiplied by the number of drinks ordered, which is dd

Total cost=$0.93ff+$1.11dd

Now to determine the total cost of 4 orders of fries and 3 drinks, we simply substitute for the values of ff,4 and dd,3

Total cost=($0.93*4)+($1.11*3)

Total cost=$7.05

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Answer:

See below ~

Step-by-step explanation:

Solving for F

Finding F when K = 310.15 K

Answer:

Hyperbola

Step-by-step explanation:

Sorry if incorect

Hope this helps

Answer:

the height is 5 and the base is 17.

Step-by-step explanation:

X + 1 is the height and 4x + 1 is the base, so we can substitute this into an equation:

( x + 1 ) (4x + 1) = 85

{apply the distributive law}

4x² + x + 4x + 1 =

4x² + 5x + 1 = 85

Take 85 to the other side by -85 each side:

4x² + 5x + 1 - 85 = 85 - 85

4x² + 5x - 84 = 0

{Now we have a quadratic equation}

The roots are either -5.25 or 4. X must be 4 since it must be positive as it is a side length.

Substitute x into the base and height to get the answers.

X + 1 = 4 + 1 = 5

4x + 1 = 16 + 1 = 17

Therefore the height is 5 and the base is 17.

Answer:

0

Step-by-step explanation:

Answer: 2.5 meters long

Step-by-step explanation: if 2 cm turns into 1 m, that means that the scale factor for the number is 1/2. 5 * 1/2 = 2.5. Then just convert the cm into m.

Answer: The wall is actually 2.5 meters tall.

Step-by-step explanation: Given that in the picture the broom is 2cm long and in reality the broom measures 1 meter long, along with the fact that 100cm equals 1 meter, we can calculate that anything in reality will be 50 times greater than in the picture.

From there, simply multiply the height of the wall by 50 in order to get the real-life height of the wall (5cm), which is 2.5 meters tall.

\(0.02*50=1\)

\(0.05*50=2.5\)

Hope this helps!

Answer:

where is the question

Step-by-step explanation:

Answer:

Could be literally anything.

Step-by-step explanation:

"S" is a variable. All letters can be used, "S" has just been randomly picked. In mathematics, a variable is a symbol which functions as a placeholder for varying expression or quantities, and is often used to represent an arbitrary element of a set. In addition to numbers, variables are commonly used to represent vectors, matrices and functions.

The iterated integral is 128 when it is converted to the polar coordinates integral( upper= a, lower= 0) integral.

Polar coordinate systems are those in which each point on a two-dimensional coordinate system's plane is determined by its distance from the reference point and an angle is taken from that reference direction. The point of reference is Pole. The line segment ray from the pole in the direction of the reference is known as the polar axis.

here ,

given integrated integral is

x\(x\sqrt{x^{2} + y^{2} } dydx\)

where r is a half circle in the xy plane

the circe is  y = \(\sqrt{4 - x^{2} }\)

\(y^{2}\) = 4 - \(x^{2}\)

\(x^{2} + y^{2}\) = 4

= 16 [ -4 ] [ -2]

= 16 ( 8 )

= 128

As a result, the iterated integral is 128 when it is converted to the polar coordinates integral( upper= a, lower= 0) integral.

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According to the picture, we can find the length of PX by using the pythagorean theorem, where PX would be the hypotenuse.

The length of PX is 10 cm

This is a right-tailed test because the alternative hypothesis is H.: μ' > 0. Therefore, the correct option is H.: μ' > 0..

The hypothesis test conducted by Kayla Greene is a right-tailed test because the alternative hypothesis is H.: μ' > 0 is the correct option.

The null hypothesis in this test is H0: μ1 = μ2.

Alternative hypothesis in this test is

Ha: μ1 < μ2 (left-tailed),

μ1 ≠ μ2 (two-tailed),

μ1 > μ2 (right-tailed)

since Kayla wants to know if the population mean monthly number of kilowatt hours used per residential customer in 2017 has increased compared to that in 2006.

The population standard deviations and the results from the samples are provided in the accompanying table.

Therefore, the correct option is H.: μ' > 0..

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Answer:

25 pieces

Step-by-step explanation:

let c = amt of candy

(c - 10 ) / 5 = 3

cross-multiply:

c-10 = 15

c = 25

Answer:

5/3

Step-by-step explanation:

The slope is the coefficient next to the x. Therefore, the slope is 5/3.

Answer:

m= 5/3

Step-by-step explanation:

Math wizzz

Worked it out

And online calculator verified!

Answer:

Z = 3

Step-by-step explanation:

if y = 3 then 3 x 2 = 6 subtract that from 9 and u get 3 so therefore z is 3

Answer:

a square, I think that's the answer you're looking for

Answer:

1. the range is 68

2. the iqr is 37.5

3. the mode is 17

4. the mean is 52

5. the median is 44

6. min=7

q1=17

median=39

q3=55

max=62

iqr=38

7. data set a: q1=2 median=4 q3=5 iqr=3

data set b: q1=1 median=5 q3=7 iqr=6

Step-by-step explanation:

1. in order to find the range you subtract the largest number from the smallest number in this case its 81-13

2. you need to put the numbers from smallest to largest then you find the first quartile and the third quartile in this case it would be q1=(8+12)/2 =10 and q3= (39+56)/2=47.5

then you find the iqr by subtracting q1 from q3 so q3-q1= IQR

3. the mode is the number that shows up the most

4. to find the mean you have to add up all the numbers than divide it by how many numbers there are so all the numbers add up to 260 and you divide that by 5

5. to find the median you need to put the numbers from smallest to largest and the number in the middle is the median

i hope i helped! and for 6 and 7 you just do everything i mentioned above :)

Therefore , the solution of the given problem of triangle comes out to be KY = 16/3 inches , ZJ = 8 inches and  LY =2.66 inches.

The fact that a triangle contains four or segments qualifies it as a polygon. It is an elementary geometric form. Triangle ABC is the name given to a square with angles A, B, or C. Euclidean geometry creates one plane and square when side are not collinear. It is a polygonal if a triangle includes three sides + three corners. The intersection of a triangle's three sides is at its corners. Three triangle angles added together equal 180 degrees.

Here,

Given : A triangle XYZ

side length XY = 8 inches

and ZX = 12 inches

So,

Using centroid theorem:

We get

=> KY = 2/3 * 8

=> KY = 16/3 inches

and

=> ZJ = 2/3 * 12

=> ZJ = 8 inches

and For LY

=>  8 - 16/3

=> 2.66 inches

Therefore , the solution of the given problem of triangle comes out to be

KY = 16/3 inches , ZJ = 8 inches and  LY =2.66 inches.

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The area of the figure is 203 square km.

We have to determine

What is the area of this figure?

The area of the complex figure is determined in the three steps than adding all areas to get the area of the hole figure.

The area of the given figure is determined by the following formula;

\(\rm Area = length \times width\)

The width of the first part is 3 km and the length is 4km.

\(\rm Area = length \times width\\\\Area = 3 \times 4\\\\Area = 12\)

The width of the second part is = 3+ 9 = 12 km

And the length of the second part is 6 km.

\(\rm Area = length \times width\\\\Area = 12 \times 6\\\\Area = 72\)

The width of the third part is = 3+ 9 + 5 = 17 km

And the length of the third part is 7 km.

\(\rm Area = length \times width\\\\Area = 17 \times 7\\\\Area = 117\)

Therefore,

The area of the given figure is;

= 12 + 72 + 117 = 203

Hence, the area of the figure is 203 square km.

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If you detect the electron passing through the left slit in a double-slit experiment, the probabilities associated with it will depend on the specific setup and conditions of the experiment.

In a basic double-slit experiment, where a beam of electrons or particles is directed towards two slits, the probability of detecting the particle at a particular location on the screen depends on the interference pattern formed by the interaction of the wave-like nature of the particles. When the electron passes through the left slit, it implies that the particle's wavefunction has "collapsed" or "localized" to a specific position associated with the left slit. In this case, the probability of detecting the electron at a specific location on the screen will be concentrated around the corresponding position associated with the left slit. The probability distribution on the screen will generally show a pattern characterized by a central maximum and alternating regions of constructive and destructive interference, depending on the relative distances between the slits, the screen, and the wavelength of the particle. It's important to note that the specific probabilities associated with detecting the electron at different positions on the screen will vary depending on the details of the experimental setup, such as the dimensions of the slits, the distance between the slits and the screen, and the wavelength of the particles. To determine the exact probabilities, one would need to know the specifics of the experiment and apply the principles of quantum mechanics and wave-particle duality to calculate or measure the probabilities associated with the electron passing through the left slit.

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Without knowing the specific values of A, A1, A2, and A3, it is not possible to determine whether A belongs to the span of {A1, A2, A3}.

I assume that M22 refers to the set of 2x2 matrices.

To determine whether the given vector A belongs to the span of {A1, A2, A3}, we need to see if we can find scalars c1, c2, and c3 such that:

A = c1*A1 + c2*A2 + c3*A3

If we can find such scalars, then A is in the span of {A1, A2, A3}. Otherwise, it is not.

Without knowing the specific values of A, A1, A2, and A3, it is not possible to determine whether A belongs to the span of {A1, A2, A3}.

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Fred owes $14,250 in credit card debt.

We must total up all of Fred's assets and liabilities, then subtract them to arrive at the amount he owes on his credit cards.

Let's figure it out:

Total Assets:

House (current value) = $105,900

Checking Account = $375

Vehicle (current value) = $13,500

Savings Account Value = $1,275

Total Liabilities:

Credit Card Debt = ?

Student Loans = $32,000

Personal Loans = $800

Total Assets - Total Liabilities = Net Worth

105,900 + 375 + 13,500 + 1,275 - (Credit Card Debt + 32,000 + 800) = 74,000

Solving for Credit card debt =

Credit Card Debt = 74,000 - 88,250

Credit Card Debt = -14,250 [The negative sign identifies it as a liability, as you can see.]

Therefore, Fred owes $14,250 in credit card debt.

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If you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

To calculate the monthly payment for each financing option, we'll use the information provided:

1. 0% financing for 48 months:

Since the financing is offered at 0% interest, the monthly payment can be calculated by dividing the total purchase price by the number of months.

Purchase Price: $26,050

Number of Months: 48

Monthly Payment = Purchase Price / Number of Months

Monthly Payment = $26,050 / 48 ≈ $543

Therefore, the monthly payment for the 0% financing option for 48 months is approximately $543.

2. Rebate offer and car loan at the bank:

If you choose the rebate offer, you'll need to finance the remaining balance after deducting the rebate amount. Let's calculate the remaining balance:

Purchase Price: $26,050

Rebate Offer: $2,900

Remaining Balance = Purchase Price - Rebate Offer

Remaining Balance = $26,050 - $2,900 = $23,150

Now, we'll calculate the monthly payment using the remaining balance and the loan terms from the local bank:

Remaining Balance: $23,150

Interest Rate: 5.24% (compounded monthly)

Number of Months: 48

Monthly Payment = (Remaining Balance * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

First, let's calculate the Monthly Interest Rate:

Monthly Interest Rate = Annual Interest Rate / 12

Monthly Interest Rate = 5.24% / 12 ≈ 0.437%

Now, we can calculate the Monthly Payment using the formula mentioned above:

Monthly Payment = ($23,150 * 0.437%) / (1 - (1 + 0.437%)^(-48))

Monthly Payment ≈ $557

Therefore, if you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

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The likelihood of each utility function representing actual investor preferences varies based on different factors such as risk aversion, wealth accumulation, and personal preferences.

Utility function (a) U(W) = \(W^2\) represents a preference for increasing wealth at an increasing rate, indicating risk aversion and a desire for wealth accumulation. This is a commonly observed preference among investors.

Utility function (b) U(W) = 1/W represents a preference for wealth preservation and risk aversion. It implies that the marginal utility of wealth decreases as wealth increases, which aligns with the concept of diminishing marginal utility.

Utility function (c) U(W) = -W represents a preference for taking on risk and potentially incurring losses. This utility function implies a risk-seeking behavior, which is less common among investors who typically aim to maximize their wealth.

Utility function (d) U(W) = W represents a preference for increasing wealth linearly. This utility function suggests a risk-neutral attitude where investors are indifferent to risk and aim to maximize their wealth without considering risk factors.

Utility function (e) U(W) = ln(W) represents a preference for wealth accumulation, but with a decreasing marginal utility. This logarithmic utility function reflects risk aversion and diminishing sensitivity to changes in wealth.

Utility function (f) U(W) = \(W^(1-γ)\)/(1-γ), with γ = 2, represents risk-neutral behavior. However, the likelihood of this utility function representing actual investor preferences depends on the specific value of γ chosen. If γ is different from 2, it may represent risk aversion or risk-seeking behavior.

Overall, utility functions (a), (b), (d), and (e) are more likely to align with actual investor preferences due to their consistency with risk aversion and wealth accumulation. Utility function (c) represents a less common risk-seeking behavior, and utility function (f) depends on the chosen value of γ, making it less likely to represent typical investor preferences.

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Answer:

2/h

Explanation:

Given that a tank can be filled in h hours, to determine what part of the tank can be filled in 2 hours, all we need to is divide 2 by h.

Therefore, 2/h part of the tank will be filled in 2 hours.

Answer:

Step-by-step explanation:

y = -2x - 7

-y = 2x - 13  

y = -2x + 13

parallel

Answer:

f(x)=5x[x(2x-6)-6(2x-6)]

=5x[2x^2-6x-12x+36]

=5x[2x^2-18x+36]

=10x^3-90x^2+180x

Since the function f(x) = x², g(x) include the following: D. g(x) = (1/3x)².

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a function or object is transformed, all of its points would also be transformed.

In Mathematics and Geometry, a dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Based on the graph, we can logically deduce that function g(x) can be produced by vertically stretching the parent function by a scale factor of 1/3;

g(x) = 1/3f(x)

g(x) = (1/3x)²

g(x) = (1/9)x²

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The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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