Find an expression to represent the area of the triangle below.

Counterexample: The statement is not true. For n = 41, the expression n^3 + n^2 + 41 equals 41^3 + 41^2 + 41, which is divisible by 41 and therefore not prime.

To prove or disprove the statement, we need to find a counterexample, i.e., a natural number n for which n^3 + n^2 + 41 is not prime. By substituting n = 41 into the expression, we obtain 41^3 + 41^2 + 41. This expression is divisible by 41 since it can be factored as 41(41^2 + 41 + 1). Since a prime number is only divisible by 1 and itself, this means that the expression is not prime and thus disproves the statement. Therefore, the claim that n^3 + n^2 + 41 is prime for every natural number n is false.

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Answer:

Rate of change is -1/2.

Hope this helps! :)

Answer: -1/2

Step-by-step explanation: For a function y=mx+b, m=slope, and b=y-intercept:

y=-1/2x plus 5.    Rate of change = -1/2

Answer:the answer might be C or B

Step-by-step explanation:

The given ordered pair (1,9.24) represents the ordered pair represents the monthly cost of one song. Option C is correct.

Given that,
Avery signed up for a streaming music service where there's a fixed cost for a monthly membership and a cost per song downloaded. Her total cost is given by the linear graph.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
According to the question,
9.24 is the total cost marked on the y axis so corresponding to this the value of x is 1 which represents the number of song,
So the given ordered pair describe that the cost of one song per month is $9.24.

Thus, the given ordered pair (1,9.24) represents the ordered pair represents the monthly cost of one song. Option C is correct.

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The solution to the second-order IVP consisting of the differential equation y" - y = 0 and the initial conditions y(1) = 0, y'(1) = e^(-1).

To find a solution of the second-order initial value problem (IVP) consisting of the differential equation y" - y = 0 and the given initial conditions y(1) = 0, y'(1) = e -x-1, we can follow these steps:

Determine the general solution of the differential equation y" - y = 0:

The characteristic equation is r^2 - 1 = 0. Solving this equation, we find two distinct roots: r = 1 and r = -1.

Therefore, the general solution is y(x) = c₁e^x + c₂e^(-x), where c₁ and c₂ are constants.

Apply the initial condition y(1) = 0:

Substituting x = 1 and y = 0 into the general solution:

0 = c₁e^1 + c₂e^(-1)

Dividing through by e:

0 = c₁ + c₂e^(-2)

Apply the initial condition y'(1) = e -x-1:

Differentiating the general solution:

y'(x) = c₁e^x - c₂e^(-x)

Substituting x = 1 and y' = e^(-1) into the differentiated solution:

e^(-1) = c₁e^1 - c₂e^(-1)

Dividing through by e:

e^(-2) = c₁ - c₂e^(-2)

We now have a system of two equations:

Equation 1: 0 = c₁ + c₂e^(-2)

Equation 2: e^(-2) = c₁ - c₂e^(-2)

Solving this system of equations, we can find the values of c₁ and c₂:

Adding Equation 1 and Equation 2:

0 + e^(-2) = c₁ + c₁ - c₂e^(-2)

e^(-2) = 2c₁ - c₂e^(-2)

Rearranging this equation:

2c₁ = e^(-2)(1 + c₂)

Substituting this value back into Equation 1:

0 = e^(-2)(1 + c₂) + c₂e^(-2)

0 = e^(-2) + c₂e^(-2) + c₂e^(-2)

0 = e^(-2) + 2c₂e^(-2)

-1 = 2c₂e^(-2)

Simplifying:

c₂e^(-2) = -1/2

Substituting this value back into Equation 1:

0 = c₁ - 1/2

c₁ = 1/2

Therefore, the values of c₁ and c₂ are c₁ = 1/2 and c₂ = -1/(2e^2).

Now we can write the particular solution to the IVP:

y(x) = (1/2)e^x - (1/(2e^2))e^(-x)

This is the solution to the second-order IVP consisting of the differential equation y" - y = 0 and the initial conditions y(1) = 0, y'(1) = e^(-1).

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Answer:

The average temp was 4

Step-by-step explanation:

Answer: -15.5, -32.5

Step-by-step explanation: Call the two numbers x and y, x+y=-48 and x-y=17, subtract both of them and you get 2y=31 and then divide both sides by 2 and get -15.5 for y, plug this back in the equations and get -32.5 for x, hope this helped!

Answer:

10.7

Step-by-step explanation:

Hello There!

The image shown below shows the relationship between two chords formed inside of a circle

So the product of the lengths of the lines in the same chord is equal to the product of the other length of the chords lines if that makes sense

So basically 6 * 16 = 9 * x

we can now use this equation that was just made to solve for x

6 * 16 = 96

96 = 9x

*divide each side by 9*

96/9=10.66666667 *round to the nearest tenth* 10.7

9x/x

we're left with x = 10.7

The extremizer point is x=(1,1].

Consider the problem min 22 – (21 – 2)3 + 3 subject to X2 > 1. The given problem can be written in the following form: minimize f(x)= 22 - (21 - 2)3 + 3 subject to g(x) = x2 > 1.The extremizer point is the point that satisfies the conditions that have been given in the question. Therefore, the extremizer point in this problem is x=(1,1].In order to find the extremizer point of a problem, we need to calculate the derivative of the objective function and then equate it to zero to find the point where it attains its minimum value. Here, however, we have only one point to choose from that satisfies the given constraint, so it is the extremizer point.

A point in a convex set that does not lie on any open line segment connecting two points in the set is referred to as an extreme point in mathematics.

The terms "extreme point" and "extremal point" can also mean:

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Answer:

Equities or stocks.

Step-by-step explanation:

Equities or stocks are the source of finance for a company. A company issues stocks and then the fund received from these stocks is used to run the business operations. Risk transfer is a way to minimize the self risk and transfer it to other person. When stocks are sold the risk is transferred to other person who buys the stocks.

Answer:

stock futures

Step-by-step explanation:

Answer:

well you need to have your friends personal email then login to you email and press new message once your logged in put in you friends email and you are all set

Step-by-step explanation:

In part (a), the relation R on A = {0, 1, 2, 3} is defined as R = {(0, 0), (1, 2), (2, 2)}. In part (b), the relation S on B = {a, b, c, d} is defined as S = {(a, b), (a, c), (b, c), (d, d)}. Lastly, in part (c), the relation R on A = {0, 1, 2, 3} and B = {4, 5, 6, 8} is defined as R = {(0, 4), (0, 6), (1, 8), (2, 4), (2, 5), (2, 8), (3, 4), (3, 6)}.

a) The directed graph for relation R on A = {0, 1, 2, 3} can be represented as follows:

0 -> 0

1 -> 2

2 -> 2

Here, each element of A is represented as a node, and the directed edges indicate the pairs in the relation R.

The zero-one matrix for relation R can be written as:

| 1 0 0 0 |

| 0 0 1 0 |

| 0 0 1 0 |

| 0 0 0 0 |

In this matrix, a value of 1 indicates that the corresponding pair is in the relation, and 0 indicates that it is not.

b) The directed graph for relation S on B = {a, b, c, d} is as follows:

a -> b

a -> c

b -> c

d -> d

The zero-one matrix for relation S can be written as:

| 0 1 1 0 |

| 0 0 1 0 |

| 0 0 0 0 |

| 0 0 0 1 |

c) The directed graph for relation R on A = {0, 1, 2, 3} and B = {4, 5, 6, 8} is represented as follows:

0 -> 4

0 -> 6

1 -> 8

2 -> 4

2 -> 5

2 -> 8

3 -> 4

3 -> 6

The zero-one matrix for relation R can be written as:

| 0 0 0 0 |

| 0 0 0 0 |

| 1 0 0 0 |

| 0 0 0 0 |

| 1 0 0 0 |

| 0 0 0 0 |

| 1 0 0 0 |

| 0 0 0 0 |

In this matrix, each row represents an element of A, and each column represents an element of B. A value of 1 in the matrix indicates that the corresponding pair is in the relation, and 0 indicates that it is not.

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a)The standard error of the mean is 0.85.b) the margin of error is 1.67 at 95% confidence level.

a) To calculate the standard error of the mean, the formula is given by:σx = σ / √nWhere,σ is the population standard deviation, n is the sample size√n = √50 = 7.071σx = σ / √n= 6 / 7.071σx = 0.85 (rounded to two decimal places)

b) At 95% confidence level, the margin of error is calculated by using the following formula:

ME = z* σxWhere,z* is the z-value for 95% confidence level and σx is the standard error of the mean.

The z-value for 95% confidence level is 1.96

ME = z* σx = 1.96 x 0.85

ME = 1.67 (rounded to two decimal places)

Therefore, the margin of error is 1.67 at 95% confidence level.

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Answer:

I believe the circumference is 37.699

HOPE I HELPED!

PLEASE GIVE BRAINLIEST!

Step-by-step explanation:

Answer:

37.68 cm

Step-by-step explanation:

The photo shows the diameter as 12cm

The formula for the circumference of a circle is [tex]2\pi r[/tex]

If the diameter is 12, the radius is 6

[tex]2 \pi 6[/tex] = 2 x 3.14 x 6 = 37.68

Answer: I think it’s the first choice. Foreign Language, Math/CS, and social studies

Step-by-step explanation:

Answer:

5.9

Step-by-step explanation:

Answer:

I think it is 62.

Step-by-step explanation:

Hope this helps!

Answer:

l=8k

Step-by-step explanation:

Answer:

y=8k

Step-by-step explanation:

Answer:

It is option one

Step-by-step explanation:

I don’t know why but I’m doing a quizzizz with the same question and i picked option 2 but option one was the correct answer

Answer:

y= -3

Step-by-step explanation:

Substitute x as 0

6(0)-3y=9

-3y=9

y= -3

Answer:

$9015.20

Step-by-step explanation:

A = 4000[1 + (.063/4)]^13·4

Answer:

3276

Step-by-step explanation:

4000(6.3*13)÷100

The series converges for -8 < x < -4, and the radius of convergence is 2.

To find the radius of convergence and interval of convergence of the series, we'll use the ratio test.

The series given is:

Σ (n=1 to ∞) [tex]2^{(-n)}(x + 6)^n[/tex]

We'll apply the ratio test to determine the convergence behavior:

lim(n→∞) |(a_{(n+1)})/(a_n)|

= lim(n→∞) |[tex][2^{(-(n+1)})(x + 6)^{(n+1)}] / [2^{(-n)}(x + 6)^n][/tex]|

= lim(n→∞) |[tex][2^{(-(n+1)})(x + 6)] / [2^{(-n)}][/tex]|

= lim(n→∞) |(x + 6)/2|

To ensure convergence, we need the above limit to be less than 1:

|(x + 6)/2| < 1

Now, let's consider the cases when the above inequality holds true:

Case 1: (x + 6)/2 < 1

Simplifying, we get:

x + 6 < 2

x < -4

Case 2: -(x + 6)/2 < 1

Simplifying, we get:

x + 6 > -2

x > -8

Combining the results from both cases, we have:

-8 < x < -4

Therefore, the interval of convergence is -8 < x < -4.

To find the radius of convergence, we consider the endpoints of the interval of convergence (-8 and -4). The radius of convergence (R) is half the length of the interval of convergence.

R = (|-8 - (-4)|)/2

  = 4/2

  = 2

Hence, the radius of convergence is 2.

In summary, the series converges for -8 < x < -4, and the radius of convergence is 2.

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Answer:

The total distance the students ran in the race would be 5 1/2 km.

Step-by-step explanation:

2/4 + 3/4 + 2 2/4 + 1 3/4 = 3 10/4 = 5 2/4 = 5 1/2 (Simplified)

Answer:

6.5y + 10

Step-by-step explanation:

0.5y + 10.5 + 6.5y - 0.5 - 0.5y

combine like terms

6.5y + 10

Answer:

m

Step-by-step explanation:

f

Answer:

x<-8

Step-by-step explanation:

x/8<-1

x<-1×8

x<-8

The power series representation of f(x) = (x - 4)² is f(x) = 9 - 6x + x² + ..., and the radius of convergence, R, is infinity (∞).

To find a power series representation for the function f(x) = (x - 4)², we can expand it using the binomial theorem.

The binomial theorem states that for any real number r and a real number x such that |x| < 1, we have:

[tex](1 + x)^r[/tex] = 1 + rx + (r(r-1))/2! * x² + (r(r-1)(r-2))/3! * x³ + ...

In our case, we have f(x) = (x - 4)², which can be rewritten as (1 + (x - 4))². Using the binomial theorem with r = 2, we get:

f(x) = (1 + (x - 4))² = 1 + 2(x - 4) + (2(2-1))/2! * (x - 4)² + ...

Simplifying this expression, we have:

f(x) = 1 + 2x - 8 + (2/2) * (x² - 8x + 16) + ...

Expanding further, we get:

f(x) = 1 + 2x - 8 + x² - 8x + 16 + ...

Now we can write the power series representation of f(x) as:

f(x) = 9 - 6x + x² + ...

To determine the radius of convergence, R, we need to find the interval of x for which the series converges. In this case, the series converges for all real numbers x since there are no terms involving powers of x that could cause divergence.

Therefore, the radius of convergence, R, is infinity (∞).

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Answer:

B.

Step-by-step explanation:

hope this helps!!

The probability density function (PDF) of the random variable Z, defined as the maximum of X and Y, can be determined as follows:

For z < 0 or z > 2: fz(z) = 0

For 0 < z < 1: fz(z) = z

For 1 < z < 2: fz(z) = 2 - z

To find the PDF of Z, we need to consider the different regions of the interval [0, 2] and determine the probability density function for each region.

For z < 0 or z > 2:

Since Z cannot be less than 0 or greater than 2, the probability density in these regions is 0. Therefore, fz(z) = 0 for z < 0 or z > 2.

For 0 < z < 1:

In this range, the maximum of X and Y is always Y because Y ranges from 0 to 2. Therefore, we can write fz(z) = P(Z < z) = P(Y < z). Since Y is uniformly distributed on (0, 2), its PDF is constant within this range. The probability of Y being less than z is given by the ratio of the length of the interval (0, z) to the length of the interval (0, 2), which is z/2. Therefore, fz(z) = z/2 for 0 < z < 1.

For 1 < z < 2:

In this range, the maximum of X and Y can either be X or Y. To determine the PDF, we need to consider the probability of X being the maximum and the probability of Y being the maximum.

Probability of X being the maximum:

Since X is uniformly distributed on [0, 1], the probability of X being less than z is given by the ratio of the length of the interval (0, z) to the length of the interval (0, 1), which is z/1 = z. Therefore, the probability of X being the maximum is z.

Probability of Y being the maximum:

Since Y is uniformly distributed on (0, 2), the probability of Y being less than z is given by the ratio of the length of the interval (0, z) to the length of the interval (0, 2), which is z/2. Therefore, the probability of Y being the maximum is z/2.

Since X and Y are independent, we can add their probabilities to find the overall probability of Z being less than z. Therefore, fz(z) = P(Z < z) = P(X < z) + P(Y < z) = z + z/2 = 2z/2 + z/2 = (3z)/2.

To find the PDF fz(z) in this range, we need to calculate the derivative of the cumulative distribution function (CDF). The CDF of Z can be obtained by integrating the PDF fz(z):

Fz(z) = ∫[0,z] fz(u) du

Taking the derivative of Fz(z) with respect to z, we get:

fz(z) = d/dz (Fz(z)) = d/dz ∫[0,z] fz(u) du = d/dz (3z^2/4) = 3z/2.

Therefore, fz(z) = 3z/2 for 1 < z < 2.

For z < 0 or z > 2: fz(z) = 0

For 0 < z < 1: fz(z

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The expected number of days with non-sunny weather is given as:

E(x) = P(1) + 2P(2)

= 0.26 + 2 × 0.204

= 0.668.

Hence, this is the required answer.

1 Register should be kept open.

(10)a. The expected daily revenue for the MiniGolf $1,920.

(10)b. The average number of days the weather will not be sunny is 0.668.

9. Calculation of the number of registers:

Given that

λ = 18 customers/hour

µ = 1 / 4 min

= 15 customers/hour

So,

λ / µ = 18 / 15

= 1.2

It is given that s is the number of servers we are looking for.

Let's start solving the queuing system:

For calculating the optimal number of cash registers we have the formula;

rho = λ / (s × µ)

Where,ρ = Traffic Intensity

λ = Arrival Rate

µ = Service Rate

The number of Servers (s) is calculated as:

s = ρλ / µ(If s is fractional, round it up to the nearest integer)

Calculation of ρ;

ρ = λ / (s × µ)

= 18 / (s × 15)

For the above equation let's put some values of s to find the value of ρ;s ρ=λ/(s×µ)

18/(15s)=1.2/1.8

= 0.67, rounded up to 1.1.

The register should be kept open.

10.  Calculation of expected daily revenue:

(a) Given that revenue on a sunny day is $2,000.

If it's cloudy, the revenue decreases by 20%, and if it's rainy, the revenue decreases by 80%.

Therefore, Revenue on a cloudy day

= $2,000 - 20% of $2,000

= $2,000 - $400

= $1,600

Revenue on a rainy day = $2,000 - 80% of $2,000= $2,000 - $1,600 = $400

Now, We have to find the expected revenue for the day if it's sunny today.

There is an 80% chance of sunshine tomorrow, which means that there is (a) 20% chance of rain or cloudy weather.

Based on this, Expected Revenue for the day

= 80% of $2,000 + 20% of ($1,600 + $400)

= $1,920

(b) Calculation of the average number of days with non-sunny weather:

Let x be the number of days the weather is not sunny.

Using the probabilities given in the question, the Probability that tomorrow will be sunny if it is sunny today = 80%

The probability that tomorrow will be rainy if it is cloudy today = 20%

The probability that tomorrow will be sunny if it is cloudy today = 30%

The probability that tomorrow will be rainy if it is cloudy today = 20%

The probability that the weather will not be sunny tomorrow if it's rainy today = 80%

Therefore, the Probability of non-sunny weather in a day,

P(x) is given as follows:

P(0) = 0.8 (When it's sunny today, there's an 80% chance it'll be sunny tomorrow)

P(1) = 0.2 × 0.3 + 0.8 × 0.2

= 0.26 (When it's cloudy today, there's a 30% chance it'll be sunny tomorrow and a 20% chance it'll be rainy)

P(2) = 0.2 × 0.7 × 0.1 + 0.8 × 0.2 × 0.2 + 0.2 × 0.3 × 0.2 + 0.8 × 0.8 × 0.1

= 0.204 (When it's rainy today, there's a 10% chance it'll be sunny tomorrow and an 80% chance it'll be rainy tomorrow).

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Answer:

-5x-10 is the expression. the missing values would be 2 and -x i believe

The interval [μ - z (σ/sqrt(n)), μ + z (σ/sqrt(n))] within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.

a. The interval is [166.01, 179.99].

b. The interval is [849.07, 898.93].

c. The interval is [74.47, 77.53].

a. μ = 173, σ = 20, n = 42.

Here, we have, μ = 173, σ = 20, n = 42.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 173 - 1.96(20/sqrt(42)) , 173 + 1.96(20/sqrt(42)) ]

i.e [ 166.01, 179.99 ]

Therefore, the interval is [166.01, 179.99].

b. μ = 874, σ = 12, n = 7.

Here, we have, μ = 874, σ = 12, n = 7.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 874 - 1.96(12/sqrt(7)) , 874 + 1.96(12/sqrt(7)) ]

i.e [ 849.07, 898.93 ]

Therefore, the interval is [849.07, 898.93].

c. μ = 76, σ = 2, n = 26.

Here, we have, μ = 76, σ = 2, n = 26.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 76 - 1.96(2/sqrt(26)) , 76 + 1.96(2/sqrt(26)) ].

i.e [ 74.47, 77.53 ]

Therefore, the interval is [74.47, 77.53].

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