Ms. Williams counted students by eye color. The table shows how many students had each eye color.


Brown 21
Blue 6
Green 3


Write a ratio to compare green eyes to brown eyes.
21:30
1:7
1 over 2
21 to 3

The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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The expression can be used Jake paid each night for the hotel is:

x = d/5 - $50

Now, According to the question:

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The given data is:

He bought a plane ticket for $250 and stayed in a hotel for 5 nights.

The price d is equal to $250 + 5 prices of staying in a hotel for a night.

If we let "x" be the price per night then we can get the following:

The expression will be:

d = $250 + 5x

5x = d - $250

\(x = \frac{d - 250}{5}\)

x = d/5 - $50

Hence, The expression can be used Jake paid each night for the hotel is:

x = d/5 - $50.

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Answer:

(6)

Step-by-step explanation:

5×=20+10=

5×=30=

×=6

In order to compute the probabilities P(X > 5) and P(X < 16) for a normal random variable X with mean (mu) of 10 and variance (sigma squared) of 36, we can use the properties of the normal distribution.

In the first case, we need to calculate the probability of X being greater than 5. This can be done by standardizing the variable X using the z-score formula: z = (X - mu) / sigma. Plugging in the given values, we get z = (5 - 10) / 6 = -5/6 = -0.8333. By looking up the corresponding value in the standard normal distribution table, we find that the area to the left of z = -0.8333 is approximately 0.2033. Since we are interested in the probability of X being greater than 5, we subtract this value from 1: P(X > 5) ≈ 1 - 0.2033 = 0.7967.

In the second case, we want to calculate the probability of X being less than 16. Using the same approach, we standardize the variable X: z = (16 - 10) / 6 = 1. By referencing the standard normal distribution table, we find that the area to the left of z = 1 is approximately 0.8413. Therefore, P(X < 16) ≈ 0.8413.

To summarize, the probability that X is greater than 5 is approximately 0.7967, while the probability that X is less than 16 is approximately 0.8413.

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(a) Expected utility is calculated as the weighted average of the utilities of all possible outcomes.

According to the problem, Sam's utility function is u(100) = 1 and u(200) = 2.

The lottery L1 = ( £100, w.p. 0.6; £200, w.p. 0.4 ) has two outcomes with the probabilities of 0.6 and 0.4.

Therefore, the expected utility of the lottery L1 is:

Expected utility of L1 = 0.6 × u(100) + 0.4 × u(200)= 0.6 × 1 + 0.4 × 2= 1.4

Since Sam is willing to pay at most £120 for the lottery L1, this indicates that the expected utility of L1 is worth £120 to Sam. Thus:1.4 = u(£120)

Since we know u(100) = 1 and u(200) = 2, we can linearly interpolate to find u(£120):

u(£120) = u(100) + [(120 - 100)/(200 - 100)] × (u(200) - u(100))= 1 + [(120 - 100)/(200 - 100)] × (2 - 1)= 1.3

Therefore, the expected utility of the lottery L2 = ( £100, w.p. 0.6; £120, w.p. 0.4 ) is:

Expected utility of L2 = 0.6 × u(100) + 0.4 × u(£120)= 0.6 × 1 + 0.4 × 1.3= 0.78

So, Sam's expected utility for the lottery L2 is 0.78

.(b) The risk preferences of Sam can be determined by comparing the utility of the lottery L1 and the sure outcome that gives the same expected value as the lottery L1.

The expected value of the lottery L1 is:Expected value of L1 = 0.6 × £100 + 0.4 × £200= £140

Therefore, Sam needs to be indifferent between the lottery L1 and the sure outcome of receiving £140. Since the expected utility of L1 is 1.4, Sam's utility for receiving £140 must also be 1.4.

This can be represented as:u(£140) = 1.4From part (a), we know that u(£120) = 1.3.

Therefore, the difference between the two utility values is:u(£140) - u(£120) = 1.4 - 1.3= 0.1

The difference in utility is positive but not enough to reflect risk-loving behavior. Therefore, Sam is risk-averse.

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Step-by-step explanation:

the average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

so,

(h(7) - (h(3)) / (7 - 3)

h(7) = 7² - 7×7 + 6 = 49 - 49 + 6 = 6

h(3) = 3² - 7×3 + 6 = 9 - 21 + 6 = -6

7 - 3 = 4

(6 - -6)/4 = 12/4 = 3

the average change rate in that interval is 3 (or fully 3/1).

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

a) Equation:

b) Value of b ( base ): 3. 25

c) Growth or decay: Growth

d) y-intercept: ( 1, 0)

e) Key point : ( 1, 3. 25)

f) Horizontal Asymptote:

g) Domain:

h) Range:

The ANOVA produced 21 degrees of freedom within three treatment conditions with equal sample sizes. Therefore, each sample contains 8 individuals. So, the correct answer is D).

The formula for calculating degrees of freedom within a one-way ANOVA is

dfwithin = (N - k)

where N is the total number of observations (across all groups) and k is the number of groups being compared.

In this case, we know that dfwithin = 21, and since there are three treatment conditions being compared, k = 3

So, we can rearrange the formula to solve for N:

N = dfwithin + k

N = 21 + 3

N = 24

Since we are told that the sample sizes are all the same, we can divide the total number of observations by the number of groups to get the size of each sample

n = N/k

n = 24/3

n = 8

Therefore, there are 8 individuals in each sample. The answer is (d) 8.

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Answer:

29 degrees

Step-by-step explanation:

The arc intercepted by inscribed angle x = 360 -180 -122 = 58 degrees

   inscribed angles intercept twice as many degrees of arc

      x = 58/2 = 29 degrees

Answer:

A

Step-by-step explanation:

#5: This is a function. It passes the vertical line test.

#6: This is not a function. It does not pass the vertical line test. For example, x=0 has six y-values paired with that one x-value. A function that does not make.

#7: This passes the vertical line test.

To eliminate the parameter and express the parametric equations in the form y = f(x), we need to solve for t in terms of x and substitute it into the equation for y.

From the given parametric equations, we have:

x = e^(-2t)   ---- (1)

y = 6e^(4t)   ---- (2)

To eliminate t, we can take the natural logarithm (ln) of equation (1):

ln(x) = ln(e^(-2t))

ln(x) = -2t

t = -ln(x)/2

Now we can substitute this value of t into equation (2):

y = 6e^(4(-ln(x)/2))

y = 6e^(-2ln(x))

y = 6(x^(-2))

Therefore, the parametric equations x = e^(-2t) and y = 6e^(4t) can be expressed in the form y = f(x) as y = 6(x^(-2)).

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The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

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Answer:

please see photo attached for detailed analysis.

Answer:

5. 2=1+1

6. 0= -3*0

7.2=3*0+2

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The area of triangle ΔKLM is approximately 22.7 square inches.

To calculate the area of triangle ΔKLM, we can use the formula for the area of a triangle: A = (1/2) * base * height.

Given that the length of KL (the base) is 8.1 inches and LM (the height) is 6.6 inches, we can substitute these values into the formula:

A = (1/2) * 8.1 inches * 6.6 inches

A = 0.5 * 8.1 inches * 6.6 inches

A = 26.73 square inches

Since we need to round the answer to the nearest 10th of a square inch, the area of triangle ΔKLM is approximately 26.7 square inches.

The area of triangle ΔKLM is approximately 22.7 square inches.

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The total interest of the investment is £30.

From the question statement,, we have

Principal, P = 500

Time, t = 2 years

Rate, r = 3%

The formula for simple interest is:

I = Prt

where I is the interest, P is the principal (the amount of money invested), r is the interest rate (as a decimal), and t is the time in years.

In this case, P = £500, r = 0.03 (since the interest rate is 3%), and t = 2 years.

Plugging in these values, we get:

I  = £500 x 0.03 x 2

Evaluate

I = £30

Therefore, the total interest earned after 2 years is £30.

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The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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Answer:

D

Step-by-step explanation:

The y-coordinate will be the average of 5 and -2 which is 3/2. This eliminates options A and B. C doesn't make sense because the x-coordinate (which is -7) of the midpoint can't be larger or smaller than the x-coordinates of the endpoints, so that means that the answer is D.

Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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Answer:

There are 192 employees in the company.

Step-by-step explanation:

Let x be the total number of employees

Use ratio and proportion

\(\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192\)

x = 192

Answer: C

Step-by-step explanation:

The local weather sells the tickets the play rate of $38 and patrons attend multiple shows to encourage the buyers giving them a discount of 20$ each. The rogers has to attend the shows same year.

Hence the option B is correct.

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Answer:

No solution

Step-by-step explanation:

4x + 2(2x - 3) = 8(x - 1)

4x + 4x - 6 = 8x - 8

8x - 6 = 8x - 8

0 = -2

There is no value of x makes the equation true.

Answer:

g(x) - f(x) = 3^x - 9 - (5x - 1) = 3^x -5x - 8

The number of people who prefer eggs is 35.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent. A ratio might be formatted as a Part to Part or Part to Whole comparison. A Part to Part comparison looks at two individual quantities within a ratio of greater than two numbers, such as the number of dogs to the number of cats in a poll of pet type in an animal clinic. A Part to Whole comparison measures the number of one quantity against the total, such as the number of dogs to the total number of pets in the clinic.

Let the number of people who prefer eggs be x.

21 people said they prefer oatmeal.

The ratio of people who prefer oatmeal to those who prefer eggs is 3 to 5.

∴ \(\frac{21}{x} = \frac{3}{5} \\x = \frac{21*5}{3}\\ x = \frac{105}{3} \\x = 35\)

Thus, the number of people who prefer eggs is 35.

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Answer:

(6.25\(\pi\) + 25)cm is the exact answer

44.625 cm is an approximation

Step-by-step explanation:

c = circumference (perimeter)

d = diameter

C = \(\frac{\pi d}{4}\)

C = \(\frac{25\pi }{4}\) = 6.25\(\pi\) This is the exact answer

That would be the curved part of the pi.  Then we need to add the 2 sides which would be \(\frac{25}{2}\) + \(\frac{25}{2}\) = \(\frac{50}{2}\) = 25  The sides are the length of the radius which is half of the diameter.

(6.25\(\pi\) + 25)cm is the exact answer

If we use 3.14 for \(\pi\) The approximate answer would be:

6.25(3.14) + 25

19.625 + 25

44.625 cm is an approximation