Find the surface area and volume of a cylinder with a diameter equal
to 14 cm and a height equal to 10 cm.

The limit of the function As x → - ∞, f(x) → 2.

The limit of a function is the value the function tends to as the independent variable tends to a given value.

Given the graph of the function above, to find the limit of the function As x → -∞, f(x) →? We proceed as follows

Looking at the graph, we see that f(x) has a horizontal asymptote at y = 2. Now, we see that As x → -∞, f(x) approaches 2.

So, As x → - ∞, f(x) → 2.

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Answer:

Step-by-step explanation:

To calculate the probability of winning any amount of money, we need to sum up the probabilities of winning each individual prize.

Given the probabilities stated on the game card:

Probability of winning $10 prize = 0.2

Probability of winning $5 prize = 0.1

Probability of winning $0 prize = 0.7

To find the probability of winning any amount of money, we add these probabilities together:

0.2 + 0.1 + 0.7 = 1

The sum of the probabilities is 1, which indicates that the total probability of winning any amount of money is 1 or 100%.

Therefore, the probability of winning any amount of money in this game is 100%.

Hope this answer your question

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Answer:

(a) The value of E (X) is 4/7.

    The value of V (X) is 3/98.

(b) The value of P (X ≤ 0.5) is 0.3438.

Step-by-step explanation:

The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.

The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.

The probability density function of X is as follows:

\(f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0\)

Here, B (α, β) is:

\(B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}\)

            \(=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}\)

So, the pdf of X is:

\(f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1\)

(a)

Compute the value of E (X) as follows:

\(E (X)=\frac{\alpha }{\alpha +\beta }\)

         \(=\frac{4}{4+3}\\\\=\frac{4}{7}\)

The value of E (X) is 4/7.

Compute the value of V (X) as follows:

\(V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}\)

         \(=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}\)

The value of V (X) is 3/98.

(b)

Compute the value of P (X ≤ 0.5) as follows:

\(P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx\)

                    \(=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438\)

Thus, the value of P (X ≤ 0.5) is 0.3438.

Answer:

Someone hurry and help me and this person answer this becuase this s on my test  and we need help

Step-by-step explanation:

Answer:

C. y<3

Step-by-step explanation

got it right on edge

Answer:

24 ÷ ( 8 - 2 )

= 24 ÷ 6

= 4

so, 4 is the answer

Answer:

on your question it says “=“ but on the picture it says “÷”

so for 24=(8-12) it would be 30

and for 24÷ (8-12) it would be -6

Step-by-step explanation:

Hope this helps, have a good day

Answer:

Simplify:=-1

Step-by-step explanation:

Answer:

3j+5d

if this was helpful please mark brainliest. Have a great day.

Answer:

3j+5d

lol.............

The percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $484,500.00 and a 6.5% APR is 31.0%. (Option A)

To calculate the  percent decrease, we can use the following formula.

Percent decrease = ( (30-year factor -   15-year factor) / 30-year factor) x 100

Substituting the values from the chart.  

= (($ 6.65 - $8.71) / $6.65) x 100

= ( -$ 2.06 / $6.65) * 100

= -0.309 *  100

Percent decrease ≈ - 30.9 %

Since the question asks for the percent decrease as a positive value, we take the absolute value of the result which is

Percent decrease ≈ 31%

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The value of the fraction expression -2 1/2 - (-4 3/5) is 2 1/10

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

−2 /2/1 −(−4 3/5)

Express properly

So, we have the following representation

-2 1/2 - (-4 3/5)

Remove the brackets

This gives

-2 1/2 - (-4 3/5) = -2 1/2 + 4 3/5

Express the denominator as 10

So, we have

-2 1/2 - (-4 3/5) = -2 5/10 + 4 6/10

Evaluate the difference

-2 1/2 - (-4 3/5) = 2 1/10

Hence, the solution is 2 1/10

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The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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The x-intercepts represent a zero profit, the maximum value of the graph represents the maximum profit, An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5 and the domain is constrained by x=0.

Part A:

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

Part B:

An approximate average rate of change of the graph from x=3  to x=5 represents the reduction in profit from 3 to 5.

Part C:

Simply, the domain is constrained by x=0.

We are obliged at x=6 .

This is because we have to avoid a negative profit.

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\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108\)

Answer:

x = -2, y = -3

Step-by-step explanation:

y - 3x = 3

x - 2y = 4

-3x + y = 3

x - 2y = 4

-6x + 2y = 6

x - 2y = 4

Add the equations.

-5x = 10

x = -2

Substitute -2 for x in the first original equation and solve for y.

y - 3x = 3

y - 3(-2) = 3

y + 6 = 3

y = -3

Answer: x = -2, y = -3

Step-by-step explanation:

\(y-3x=3--------(1) \\ x-2y=4 --------(2)\\ -3x +y =3 ----------(1)\\x-2y =4-----------(2)\\Multiply -equation(1)-by-the-coefficient-of x -in-equation(2)\\Multiply -equation(2)-by-the-coefficient-of x -in-equation(1)\\ -3x +y =3 ----------(1)\times 1\\x-2y =4-----------(2)\times -3\\\\-3x+y = 3 -----(3)\\-3x +6y = -12----(4)\\Subtract -equation(4)-from-equation(3)\\-5y =15\\\frac{-5y}{-5} =\frac{15}{-5} \\y = -3\\\)

\(Substitute ; -3 -for;y -in -equation (1) or (2)\\-3x +y =3 ----------(1)\\-3x + (-3)=3\\-3x-3 =3\\-3x= 3+3\\-3x=9\\\frac{-3x}{-3} = \frac{9}{3} \\x = -2\)

Answer:

D is correct

Step-by-step explanation:

p=q  then q is the same as p and if r=p that is true

Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Answer:

Aircraft A: 403 seats

Aircraft B: 298 seats

Step-by-step explanation:

Let's x represent the seats in Aircraft B

We have the equations:

Aircraft A: (x + 105)

Aircraft B: x

We Know

Their total number of seats is 701; find the number of seats for each aircraft.

We Take

x + (x + 105) = 701

2x + 105 = 701

2x = 596

x = 298 seats

So, there are 298 seats in Aircraft B

Aircraft A has how many seats?

We Take

701 - 298 = 403 seats

So, there are 403 seats in Aircraft A

Final Answers:

Aircraft A: 403 seats

Aircraft B: 298 seats

Answer:

A. 6

Step-by-step explanation:

We see that 20 is a diameter that goes through the center of the point. This means that the top half of the black line is 10 and the top half of the blue line is 8. Use the Pythagorean Theorem to find out the length of the shortest side by doing 10^2 - 8^2 = x^2. x^2 = 36; x = 6.

Answer:

This statement would be false.

Step-by-step explanation:

The given equations have slopes that are positive and negative. Therefore, we know that they will intersect at some point because the slopes are not the same. In fact, they intersect at the point (9 3/4, 1 1/2).

I have attached an image of the graph of these two equations for your reference.

Okay so you put -6 in where y is then solve and youll get your answer

-8x-7(-6)=-6

The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60

(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.

Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200

Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments

Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]

Total amount paid = $1,300 + $13,200 + $14,041.60

Total amount paid = $28,541.60

Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.

(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.

Total interest paid = Total amount paid - Total amount borrowed - Down payment

Total interest paid = $28,541.60 - $13,200 - $1,300

Total interest paid = $14,041.60

Therefore, the amount of interest Debra paid on the loan was $14,041.60.

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The system of linear equations that can be solved from the matrices is given as follows:

Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:

A = [-5 4; -8 1]

Hence the multiplication of matrices representing the system is given as follows:

[-5 4; -8 1][x; y] = [3; -6]

Applying the multiplication of matrices, the system of equations is given as follows:

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Answer:

1. 0.2

2. 0.25

3. 0.6

4. 0.8

Answer:

Step-by-step explanation:

y=ax²+bx+c

x=1,y=-5

-5=a+b+c   ...(1)

x=2,y=-3

-3=4a+2b+c   ...(2)

x=3,y=3

3=9a+3b+c  ...(3)

(2)-(1) gives

2=3a+b   ...(4)

(3)-(2) gives

6=5a+b   ...(5)

(5)-(4) gives

4=2a

a=4/2=2

from (4)

6=5(2)+b

b=6-10=-4

from (1)

-5=2+(-4)+c

-5=-2+c

c=-3

y=2x²-4x-3

We are given that the sample size $\sf\:n = 18$, sample mean $\sf\:\bar{X} = 103$, sample standard deviation $\sf\:S = 10$, and margin of error $\sf\:E = 6.05$ for a 98% confidence interval estimate for the population mean.

Using the formula for the margin of error, we can find the value of the t-score that corresponds to a 98% confidence level with 17 degrees of freedom (since we have 18 samples):

$\sf\:t_{0.01/2, 17} \implies 2.898$

Now, we can use the formula for a confidence interval estimate to find the lower and upper bounds of the interval:

$\sf\:\bar{X} - E \implies 103 - 6.05 < \mu < \bar{X} + E \implies 103 + 6.05$

Substituting in the values we have:

$\sf\:103 - 6.05 < \mu < 103 + 6.05$

Simplifying:

$\sf\leadsto\:96.95 < \mu < 109.05$

Therefore, a 98% confidence interval estimate for the population mean is $\sf\: (96.95, 109.05)$ rounded to two decimal places.

\(\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}\)

\(\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}\)

\({\bigstar{\underline{\underline{\sf{\color{red}{Sumit\:Roy}}}}}}{\bigstar}\\\)

1/6

approximately the same as

Answer:

✔1/6

✔ approximately the same as

Step-by-step explanation:

Here's proof

The categories of the solutions are

The graph represents the given parameter

As a general rule, when two lines or curves intersect, then the point of intersection represents the solution to the system of equations

In this case, the graph intersect at points B and F

This means that the solution to the system are Point B and Point F

While other points do not represent the solutions

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Answer:

j

Step-by-step explanation:

j

Answer:

A. 3 \(\frac{1}{4}\)

Step-by-step explanation:

Answer:

36 is answer

Step-by-step explanation:

36 - 36 is equal to 0

Answer: SOrry no answer im just dumb :( but lonely so hear me out. ( if u dont care just earse it )

Step-by-step explanation:

Ok I don't have any friends but I have dated a boy, he was my first bf and he broke up with me bc i text him for 7 days bc don't  have a phone and ye he broke up with me bc of that anywayss he told me he missed me and I was so stupid that I said why are u telling me this is you broke up wit me ? rightt and then 2 moths later I stared to miss him :(( i told him that I miss him but I didn't want him back but all he said was that wen did u start cathcing feeling for me? and how did u start catching feelings? and blah blah blah. soo yeah i texted him and he just leaves me on delivered even wen can see that hes active like idk just sad :(( (sorry for telling you this. its cs idk just sadddd :(((((  )