A team pays $50 to reserve a banquet table. The players on the team pay
$9 per person. The team spends a total of $104. How many players sit at
the team table? *

Joint density function is as follows: \(f(x, y) = 16y\ x3 , x > 2, 0 \leq y \leq 1\).

We need to find the marginal density function of X. Using the formula of marginal density function, \(f_X(x) = \int f(x, y) dy\)

Here, bounds of y are 0 to 1.

\(f_X(x) =\int 0 1 16y\ x3\ dyf_X(x) \\= 8x^3\)

Now, the marginal density function of X is \(8x^3\).

Marginal density function helps to find the probability of one random variable from a joint probability distribution.

To find the marginal density function of X, we need to integrate the joint density function with respect to Y and keep the bounds of Y constant. After integrating, we will get a function which is only a function of X.

The marginal density function of X can be obtained by solving this function.

Here, we have found the marginal density function of X by integrating the given joint density function with respect to Y and the bounds of Y are 0 to 1. After integrating, we get a function which is only a function of X, i.e. 8x³.

The marginal density function of X is \(8x^3\).

To know more about marginal density visit -

brainly.com/question/30651642

#SPJ11

Answer:

its In “Growing Up: Key Moments,” which piece of evidence best supports the author’s idea that challenging moments help people learn as they grow up?

Step-by-step explanation:

bc ez ez e yba better then aut

Answer:

For every one pound there are 16 ounces.

Step-by-step explanation:

We can simply see that by dividing the ounces by pounds, 32/2 = 16, and 48/3 = 16.

Number of ounces: 16, 32, 48, 64, 80, 96

Number of pounds:  1, 2, 3, 4, 5, 6

Step-by-step explanation:

The equation of a circle written in the form (x−h)2+(y−k)2=r2 where (h,k) is the center and r is the radius. The circle centered at the origin with radius 1; its equation is x2+y2=1.

Hope it help!!!

This is the required solution that satisfies the given differential equation and initial condition.

The given differential equation is f '(x) = 6x², where the initial condition is given as f(0) = −9.

We can start with integration and find the particular solution: ∫f '(x) dx = ∫6x² dx ⟹ f(x) = 2x³ + C, where C is the constant of integration.

To find the constant C, we will use the initial condition given as

f(0) = −9f(0) = 2(0)³ + C = C = -9

Therefore, the particular solution is:f(x) = 2x³ - 9

Hence, this is the required solution that satisfies the given differential equation and initial condition.

Know more about differential equation here:

https://brainly.com/question/28099315

#SPJ11

Area of the region consisting of all such line segments is 168 * pi * √t(28228).

To find the area of the region consisting of all line segments follow these steps:
1. Consider a line segment of length 336 tangent to the circle at its midpoint. Let the midpoint be point M, and the two endpoints be A and B.

2. Draw a radius from the center of the circle, O, to point M.

3. Since OM is perpendicular to the tangent line segment AB, we have a right triangle OMA with hypotenuse OA. Note that the length of OM is the radius of the circle, 2 units.

4. We are given that the length of AB is 336. Since M is the midpoint of AB, AM and MB both have lengths of 168.

5. Using the Pythagorean theorem in right triangle OMA, we get OM² + AM² = OA². Substitute the given values: 2² + 168² = OA².

6. Simplify: 4 + 28224 = OA². Thus, OA² = 28228, and OA = √(28228).

7. Now, consider all such line segments as they rotate around the circle. They form a cone with base radius 168 and slant height OA (which is √(28228)).

8. To find the area of this cone, use the formula

A = (1/2) * Circumference of base * Slant height.

The circumference of the base is 2 * pi * 168 = 336 * pi.

9. Plug in the values: A = (1/2) * 336 * pi * √(28228).

10. Simplify: A = 168 * pi * √(28228).

So, the area of the region consisting of all such line segments is 168 * pi * √(28228).

Learn more about Pythagorean theorem.

brainly.com/question/14930619

#SPJ11

Answer:

A. \(Change = Final\ temperature - Inicial\ temperature\)

B. Negative change of 18 degrees

C. Negative change of 23 degrees, final temperature would be -8°F

Step-by-step explanation:

A.

The expression that represents the change in temperature is:

\(Change = Final\ temperature - Inicial\ temperature\)

B.

If the final temperature is -3°F and the inicial temperature is 15°F, the change in temperature is:

\(Change = -3 - 15 = -18\° F\)

We have an absolute change of 18 degrees.

C.

If the change is 5 degrees more, the change would be 18 + 5 = 23 degrees, and the final temperature would be 5 degrees lower, that is:

\(Final\ temperature = -3 - 5 = -8\°F\)

Answer:

x = 16

y = 10

Step-by-step explanation:

See attached worksheet.

\(~~~~~~ \textit{Compound Interest Earned Amount}\\\\A=P\left(1+\frac{r}{n}\right)^{nt}\quad\begin{cases}A=\textit{accumulated amount}\dotfill &\$2900\\P=\textit{original amount deposited}\dotfill &\$2000\\r=rate\to 6.75\%\to \frac{6.75}{100}\dotfill &0.0675\\n=\begin{array}{llll}\textit{times it compounds per year}\\\textit{monthly, thus twelve}\end{array}\dotfill &12\\t=years\end{cases}\)

\(2900=2000\left(1+\frac{0.0675}{12}\right)^{12\cdot t}\implies \cfrac{2900}{2000}=\left(1+\frac{0.0675}{12}\right)^{12t} \\\\\\ \cfrac{29}{20}=(1.005625)^{12t}\implies \log\left( \cfrac{29}{20} \right)=\log(1.005625^{12t}) \\\\\\ \log\left( \cfrac{29}{20} \right)=t\log(1.005625^{12})\implies \cfrac{\log\left( \frac{29}{20} \right)}{\log(1.005625^{12})}=t\implies \stackrel{years}{5.5\approx t}\)

The person must leave the money in the bank until it reaches 2900 dollars for 5.5 years.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Given that,

Principal amount, P = 2000 dollars

Rate of interest, r = 6.75% = 0.0675

Final amount, A = 2900 dollars

The formula to find the final amount in a compound interest is,

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

n = number of times interest compounded in a year = 12 (Since compounded monthly.

Substituting the given values,

2900 = 2000 [1 + (0.0675/12)]^ (12t)

2900 = 2000 (1.005625)^(12t)

2900 = 2000 (1.069628)^t

(1.069628)^t = 1.45

Taking logarithms on both sides,

t = ㏒(1.45) / ㏒ (1.069628)

t = 5.52 ≈ 5.5

Hence the time that the person must keep the money is 5.5 years.

Learn more about Compound Interest here :

https://brainly.com/question/14295570

#SPJ3

The expressions in the order they would appear on a number line from least to greatest are: 11 over 9, square root of 5, square root of 11, square root of 20, 2 to the power of 3.

To determine the order of the expressions on a number line, we compare their numerical values.

Starting with the given options:

- 2 to the power of 3 equals 2³, which evaluates to 8.

- The square root of 5 is an irrational number approximately equal to 2.236.

- The square root of 20 is an irrational number approximately equal to 4.472.

- The square root of 11 is an irrational number approximately equal to 3.317.

- 11 over 9 is a fraction that simplifies to approximately 1.222.

Comparing these values, we find that 11 over 9 is the smallest. Next is the square root of 5, followed by the square root of 11. Then comes the square root of 20, and finally, 2 to the power of 3 is the largest.

learn more about expressions here:

https://brainly.com/question/4448392

#SPJ11

the complete question is:

Which shows the expressions in the order they would appear on a number line from least to greatest?

2 to the power of 3, square root of 5, square root of 20, square root of 11 11 over 9

2 to the power of 3, square root of 11, 11 over 9, square root of 20, square root of 11

11 over 9, square root of 5, square root of 11, square root of 20, 2 to the power of 3

 11 over 9, 2 to the power of 3, square root of 5, square root of 20, square root of 11

Answer:

24.67

Step-by-step explanation:

6 x 3 = 18

18 plus 6 = 24

X-M=0.60

P-3=7

24.67

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

Learn more about logarithm at: brainly.com/question/30226560

#SPJ11

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

Learn more about unit conversion at: brainly.com/question/141163

#SPJ4

The domain of the given expression is the set of all x-values for which the expression is defined. In this case, the expression is cos(x)/sin(x) = sin(x).

To determine the domain restriction, we need to consider that the denominator, sin(x), cannot be zero. Therefore, we have to exclude any x-values that make sin(x) equal to zero.

We know that sin(x) = 0 when x is equal to any multiple of π (pi). So, the domain restriction is x ≠ nπ, where n is any integer.

In other words, x can take any value except for the multiples of π/2, because those values would make the denominator zero.

Thus, the domain restriction for the given expression cos(x)/sin(x) = sin(x) is x ≠ nπ, where n is any integer.

Note: The function cot(x) is defined as cos(x)/sin(x), and its domain is the set of all real numbers except for nπ, where n is any integer.

Learn more about domain restriction

https://brainly.com/question/31280397

#SPJ11

The break-even point is the level of output at which total revenue (TR) equals total cost (TC). In this case, with TR(x) = 20x and TC(x) = 120 + 10x, we need to find the value of x where TR(x) = TC(x).

To find the break-even point, we set TR(x) equal to TC(x) and solve for x.
TR(x) = TC(x) can be expressed as:
20x = 120 + 10x
Simplifying the equation, we combine like terms:
20x - 10x = 120
10x = 120
To isolate x, we divide both sides of the equation by 10:
x = 12
Therefore, the break-even point occurs when x is equal to 12. At this level of output, the total revenue is equal to the total cost.

Learn more about break-even point here
https://brainly.com/question/32507413



#SPJ11

The value of the interquartile range for the given subsample is 8.

The interquartile range (IQR) is a measure of the dispersion of a set of observations. It is defined as the difference between the third quartile and the first quartile (Q3-Q1). The subsample data is as follows: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. The interquartile range for the subsample data can be computed as follows:

Step 1: Arrange the data in ascending order: 18, 20, 21, 22, 24, 24, 25, 27, 28, 31, 35, 36.

Step 2: Find the median of the lower half of the data, which is called the first quartile, Q1. Here, the lower half of the data is 18, 20, 21, 22, 24, and 24. Hence, the median of the lower half of the data is the average of the two middle values, which is Q1 = (22 + 21)/2 = 21.5.

Step 3: Find the median of the upper half of the data, which is called the third quartile, Q3. Here, the upper half of the data is 24, 25, 27, 28, 31, 35, and 36. Hence, the median of the upper half of the data is the average of the two middle values, which is Q3 = (28 + 31)/2 = 29.5.

Step 4: Calculate the interquartile range as the difference between the third quartile and the first quartile: IQR = Q3 - Q1 = 29.5 - 21.5 = 8.

Therefore, the value of the interquartile range for the given subsample is 8.

To learn more about interquartile range visit : https://brainly.com/question/1210750

#SPJ11

Answer:

1) 2,6,18,54,162,468 (multiply by 3 each time)

2) 2, -4, 8, -16, 32, -64 (i'm not sure what this is but i'm pretty confident i'm right lol)

3) 1,3,5,7,9,11 (add 2 each time)

4) 1, 2/3 , 4/6  , 8/9 ,  _ _ (i'm sorry i tried my hardest but i don't know this one)

Step-by-step explanation:

hope this helped! so sorry about 4...

2 + 7/8 :)

(two and seven eighths)

a. The 90% confidence interval for the mean monthly electric bills of all residents is ($88.06, $91.94).

b. The 95% confidence interval for the mean monthly electric bills of all residents is ($87.05, $92.95).

To construct the confidence intervals, we use the formula: CI = X ± zα/2 * (σ/√n), where X is the sample mean, zα/2 is the critical value of the standard normal distribution for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the critical value of zα/2 is 1.645. Plugging in the values, we get a confidence interval of ($88.06, $91.94). This means that we can be 90% confident that the true mean monthly electric bill for all residents falls between $88.06 and $91.94.

For a 95% confidence interval, the critical value of zα/2 is 1.96. Plugging in the values, we get a confidence interval of ($87.05, $92.95). This means that we can be 95% confident that the true mean monthly electric bill for all residents falls between $87.05 and $92.95.

In both cases, we can see that the confidence intervals are relatively narrow, which is a reflection of the large sample size and relatively small standard deviation of the sample. The larger the sample size and the smaller the standard deviation, the narrower the confidence interval will be.

Learn more about confidence interval:

brainly.com/question/13067956

#SPJ11

Answer

Opinion D

The answer is 4/8

Step-by-step explanation:

because

1/8 + 3/8 = 4/8

Answer:

its D im preety sure

Step-by-step explanation:

srry if im wrong

Answer: We can cut 6 \(\dfrac23\) sections  out of each piece of wood.

Step-by-step explanation:

Given: A piece of wood is 4 feet long.

Number of \(\dfrac23\) sections = \(4\div\dfrac23\)

\(=4\times\dfrac{3}{2}\ \ \ \ [\because \dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}]\\\\=2\times3\\\\=6\)

i.e. Number of \(\dfrac23\) sections = 6

Hence, we can cut 6 \(\dfrac23\) sections  out of each piece of wood.

The smallest number of eggs that could have been in the box is 1134

The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:

Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:

n ≡ 1 (mod 2)

n ≡ 1 (mod 3)

n ≡ 1 (mod 4)

n ≡ 1 (mod 5)

n ≡ 1 (mod 6)

n ≡ 0 (mod 7)

For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.

Plugging these values into the formula and simplifying modulo 5040, we get:

n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040

n = (−8946) mod 5040

n = (−3906) mod 5040

n = 1134 mod 5040

Therefore, the smallest number of eggs that could have been in the box is 1134

to know more about congruences click here:

https://brainly.com/question/30818154

#SPJ4

The measures of the corresponding inscribed angles, and then add those angles together to find the measure of angle L. Therefore, the measure of angle L is 64 degrees.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In other words, if we have an angle whose vertex is on the circumference of a circle, and whose sides intersect two points on the circumference, then the measure of the angle is half the measure of the arc between those two points.

In this problem, we are given the measures of two arcs, DR and SV, and we want to find the measure of angle L. We can start by using the Inscribed Angle Theorem to find the measures of the corresponding inscribed angles. Let's call these angles A and B, where A is the inscribed angle that intercepts arc DR, and B is the inscribed angle that intercepts arc SV.

Using the Inscribed Angle Theorem, we can find that m∠A=12m⌢DR=12(34∘)=17∘m∠B=12m⌢SV=12(94∘)=47∘

To find the measure of angle L, we simply add angles A and B together: m∠L=m∠A+m∠B=17∘+47∘=64∘

Therefore, the measure of angle L is 64 degrees.

Learn more about Measures:

brainly.com/question/2384956

#SPJ11

Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

know more about confidence interval: brainly.com/question/32546207

#SPJ11

When Gracie distributes her carrots equally among the 5 bunnies, each bunny gets 7,878 whole carrots, and 3,939 whole carrots remain without being given to a bunny. These figures are whole numbers.According to the statement, Gracie has 5 pet bunnies that love to eat whole carrots. Gracie has 3,939 carrots to feed the bunnies, and she will use as many carrots as she can and give each bunny the same number.

To calculate the number of carrots each bunny will get:Total number of whole carrots ÷ Total number of bunnies = Number of whole carrots each bunny gets Gracie distributes the 3,939 carrots equally among the 5 bunnies, with each bunny getting 7,878 carrots. This is illustrated in the calculation below:3,939 ÷ 5 = 7,878Hence, the number of whole carrots each bunny gets is 7,878.

When it comes to the number of carrots that remain without being given to a bunny, we need to calculate it using the following formula:Total number of whole carrots − (Number of whole carrots each bunny gets × Total number of bunnies) = Number of whole carrots that remain without being given to a bunnyUsing the figures from the above calculations, the computation will be as follows:3,939 − (7,878 × 5) = 3,939 − 39,390 = -35,451. Therefore, the number of whole carrots that remain without being given to a bunny is -35,451. However, since the answer must be a whole number, we can round this up to 0 carrots. This implies that all of the carrots were given to the bunnies.

Learn more about distributes:

https://brainly.com/question/29002154

#SPJ11

F(3) is equal to 9, based on the given table and the corresponding values of x and f(x). Option D.

To find the value of F(3) based on the given table, we look at the corresponding x-value of 3 and find its corresponding f(x) value.

From the table, we see that when x = 3, f(x) = 9. Therefore, F(3) = 9.

The table shows the values of x and their corresponding f(x) values. We can see that when x increases by 1, f(x) also increases by 3. This indicates that the function has a constant rate of change, where the change in f(x) is always 3 units for every 1 unit change in x.

Given that F(3) represents the value of the function when x = 3, we look at the x-values in the table and find the corresponding f(x) value. In this case, when x = 3, f(x) = 9.

Therefore, the value of F(3) is 9. Option D is correct.

For more such question on values. visit :

https://brainly.com/question/843074

#SPJ8

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

Learn more about combinations here : brainly.com/question/28065038

#SPJ11