The equation for the area of a trapezoid is a equals one-half times h times the quantity of b subscript 1 plus b subscript 2 end quantity.. if a = 18, b1 = 5, and b2 = 7, what is the height of the trapezoid? h = 1.5 h = 3 h = 6 h = 7

The interaction observed between species X and species Y is commensalism, which is an interaction between two species in which one species benefits from the other without causing any harm to it. Commensalism is a type of symbiotic relationship

Given that the change in populations of two species of animals in a habitat can be modeled by the following equations:

\frac{dx}{dt}=6x-2.5y \frac{dy}{dt}=-0.8x+3y

The interaction that we observe between the two species can be explained as follows:

Species X has a positive coefficient in the equation of its population, which means that the population size of this species increases as it is isolated from the other species (y=0).

This indicates that species X is an intraspecific interaction, which means that it can survive and increase in numbers without the presence of another species.

Species Y, on the other hand, has a negative coefficient in the equation of its population, which means that its population size decreases when it is isolated from the other species (x=0).

This indicates that species Y is an interspecific interaction, which means that it needs the presence of another species (species X) to survive and increase in numbers.

In conclusion, we can say that the interaction observed between species X and species Y is commensalism, which is an interaction between two species in which one species benefits from the other without causing any harm to it. Commensalism is a type of symbiotic relationship.

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Rachel earned an amount of $ 920

Given in the question,

5% × n = $46

5/100 × n = $46

0.05 × n =$46

0.05/0.05 × n = 46/0.05

Hence the amount is n = $920

Income that is earned comes under total earnings after taxes are deducted which one has already paid. Some of the income which is earned can include union strike benefits, specific retirement pensions, and long-term disability benefits. An expense that is removed or subtracted from the income of the person who is paying the taxes in order to lower the income which is earned by the person so that it is subjected to lower tax subtraction is known as deduction.

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The limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

To find the limit of (x + x²)/(2 − 3x²) as x approaches infinity, we can use l'Hospital's Rule.

First, we need to check if the limit is in the indeterminate form 0/0 or ∞/∞. As x approaches infinity, both the numerator (x + x²) and the denominator (2 - 3x²) approach infinity.

Therefore, the limit is in the indeterminate form ∞/∞, and we can apply l'Hospital's Rule.

l'Hospital's Rule states that if the limit is in the indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately, and then find the limit of the ratio of their derivatives.

Numerator's derivative: d/dx(x + x²) = 1 + 2x Denominator's derivative: d/dx(2 - 3x²) = -6x

Now, we'll find the limit of the ratio of their derivatives as x approaches infinity: lim (1 + 2x)/(-6x) as x→∞

We can use l'Hospital's Rule again, as this limit is also in the indeterminate form ∞/∞. Numerator's second derivative: d/dx(1 + 2x) = 2

Denominator's second derivative: d/dx(-6x) = -6

Now, we'll find the limit of the ratio of their second derivatives as x approaches infinity: lim (2)/(-6) as x→∞ Since the limit involves constants only, it does not depend on x, and we can directly compute the limit: 2 / (-6) = -1/3

Therefore, the limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

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Answer: B

Step-by-step explanation:

What you are actually paying is 100%-20% = 80%

So it's 80% of the price =

.8p

The probability of the cell phone company gaining at least 5 new customers from contacting 50 potential customers through their telemarketing campaign is approximately 42.46%.

If the probability of successfully gaining a new customer through a telemarketing campaign is 0.07, then the probability of not gaining a new customer is 0.93 (1-0.07). To calculate the probability of gaining at least 5 new customers out of 50 potential customers, we can use the binomial distribution formula.
P(X≥5) = 1 - P(X<5)
Where X is the number of new customers gained out of 50 potential customers.
P(X<5) = Σ (50 choose x) * (0.07)^x * (0.93)^(50-x) for x = 0 to 4
Using a calculator or software, we can calculate P(X<5) to be 0.906.
Therefore, the probability of gaining at least 5 new customers out of 50 potential customers is:
P(X≥5) = 1 - P(X<5) = 1 - 0.906 = 0.094
So, there is a 9.4% chance of gaining at least 5 new customers out of 50 potential customers in this telemarketing campaign.
To calculate the probability of successfully gaining at least 5 new customers from 50 potential customers with a success rate of 0.07, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where P(X = k) is the probability of k successes in n trials, C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success, and (1-p) is the probability of failure.
In this case, n = 50, p = 0.07, and we want to find the probability of at least 5 successes (k ≥ 5). To do this, we can calculate the probability of fewer than 5 successes (k < 5) and subtract this value from 1:
P(X ≥ 5) = 1 - P(X < 5)
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
Now, we can plug in the values and calculate each term using the binomial probability formula, then sum the probabilities and subtract from 1 to get the desired probability:
P(X ≥ 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))
After calculating the probabilities and summing them, we find:
P(X ≥ 5) ≈ 0.4246

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Answer:

Um because we just do :) and where human so yeah lol

Step-by-step explanation:

a(t) = 225 * 0.75^t is an exponential model representing the amount a in milligrams of the drug remaining in the patient's system after t hours.

An exponential model representing the amount of the therapeutic drug remaining in the patient's system after t hours can be written as:

a(t) = 225 * 0.75^t

This model indicates that the amount of the drug remaining in the patient's system after t hours is equal to the initial dosage of 225 milligrams multiplied by 0.75 raised to the power of t. The 0.75 term represents the decay rate of 25% per hour, which means that the amount of the drug in the patient's system decreases by 25% every hour.

For example, if t = 1, then the model would give us the amount of the drug remaining in the patient's system after 1 hour:

a(1) = 225 * 0.75^1 = 168.75 milligrams

If t = 2, then the model would give us the amount of the drug remaining in the patient's system after 2 hours:

a(2) = 225 * 0.75^2 = 126.56 milligrams

And so on. This model can be used to predict the amount of the drug remaining in the patient's system at any time t.

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Triangle with sides AB = 8cm , CA = 5cm , BC = 7cm and AB = 7cm , BC = 10cm , CA = 8cm can construct a Triangle.

Condition : For forming the triangle, the sum of two sides must be greater than the third side.

a.  AB = 4cm, CA = 3cm, BC = 10cm

   CA+BC=AB

   3+1=4

   4=4

Therefore, it cannot form a triangle because it is not satisfying the condition.

b.  AB = 8cm , CA = 5cm , BC = 7cm

    AB+CA>BC

    AB+BC>CA

    CA+BC>AB

    Therefore, it can form a triangle because it satisfies the condition.

c.  AB = 7cm, BC = 10cm, CA = 8cm

   AB+BC>CA

   AB+CA>BC

   BC+BC>AB

  Therefore, it can form triangle because it satisfies the condition.

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Answer:

3root2

Step-by-step explanation:

this is root18 = 3root2

Firstly, let’s assume the the whole capacity the work requires is 1.

Then, let’s see how 1 man can do in 50 days: 1/5.

Further, let’s see how 1 man can do in 1 day : 1/(5×50) = 1/250.

Similarly, let’s see how 1 woman can do in 1 day: 1/(10×50) = 1/500.

Now, we have 8 men, and they can do 8*1/250 in 1 day, which is 4/125.

Besides, we have 4 women, and they can do 4×1/500 in 1 day, which is 1/125.

Therefore, all people we have can do 4/125 + 1/125 of the work in 1 day, which is 1/25.

As a result, the work takes 1/(1/25)= 25 days.

Answer:

700pi

Step-by-step explanation:

2pi(10)^2+2pi(10)(25)

The correct matches for the vocabulary would be :

Apathy is a lack of interest or passion for anything. The line "Ahmein doesn't care if he does well or not" describes apathy since Ahmein is apathetic about whether he succeeds or fails.

Being competent is having the knowledge and skills required to complete a task successfully which describes Javier as he is aware that he can construct a birdhouse.

Expectations are convictions or presumptions regarding future events. Value is a term used to describe something's importance or worth.

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Answer:

1. apathy = Trudy doesn't care about doing well in school.

2. competent = Javier knows he is able to build a birdhouse.

3. expectations = fear of failure or success

4. autonomy = Alfonzo likes to make choices on his own.

5. stress = Quincy feels anxious and distressed about a test.

Answer:

Yes.

Step-by-step explanation:

As long as each input (x value) has exactly one output (y value), then it is a function.

Answer: 4.584

Step-by-step explanation:

22.92/x=100/20

(22.92/x)*x=(100/20)*x       - we multiply both sides of the equation by x

22.92=5*x       - we divide both sides of the equation by (5) to get x

22.92/5=x

4.584=x

x=4.584

Answer:

4.584

Step-by-step explanation:

Answer:

- 3 / 10

Step-by-step explanation:

- 9 / 10 - ( - 3 / 5 )

= - 9 / 10 + 3 / 5

= 3 / 5 - 9 / 10

= 6 / 10 - 9 / 10

= ( 6 - 9 ) / 10

= - 3 / 10

Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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In a regression problem, the given pairs of (x, y) indicate that there is not a clear linear relationship between x and y.

In a regression problem, the given pairs of (x, y) are:

(2, 1), (3, -1), (2, 0), (4, -2), and (4, 2).

This indicates that the goal is to find a mathematical relationship between the x and y values, typically by fitting a line or curve to the data points, in order to make predictions for future data or understand the underlying trend.

In this case, the given pairs of (x, y) indicate that there is not a clear linear relationship between x and y. This is because for some values of x, there are multiple corresponding y values, which suggests that there are other factors at play that are affecting the relationship between x and y. However, a regression model can still be created to find the best fit line or curve that approximates the relationship between x and y.

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The solution of each part of the question is given below:

a. Let C be the event that a person smokes cigars, and let S be the event that a person smokes cigarettes. The percentage of Americans who smoke either cigars, cigarettes, or both can be calculated as P(C U S), where U represents the union of two events. From the given information, P(C) = 15% and P(S) = 35%. The probability that a person smokes both cigars and cigarettes is 7%, so P(C ∩ S) = 7%.

P(C U S) = P(C) + P(S) - P(C ∩ S)

P(C U S) = 15% + 35% - 7% = 43%

So, 43% of Americans smoke either cigars, cigarettes, or both.

b. The percentage of Americans who smoke neither cigars nor cigarettes can be calculated as P(C' ∩ S'), where C' represents the complement of event C (not smoking cigars) and S' represents the complement of event S (not smoking cigarettes).

P(C' ∩ S') = 100% - P(C U S)

P(C' ∩ S') = 100% - 43% = 57%

So, 57% of Americans smoke neither cigars nor cigarettes.

c. The percentage of Americans who smoke cigars but not cigarettes can be calculated as P(C ∩ S').

P(C ∩ S') = P(C) - P(C ∩ S)

P(C ∩ S') = 15% - 7% = 8%

So, 8% of Americans smoke cigars but not cigarettes.

d. The conditional probability that a person smokes cigarettes given that he smokes cigars can be calculated as P(S | C), where S represents the event that a person smokes cigarettes and C represents the event that a person smokes cigars.

P(S | C) = P(S ∩ C) / P(C)

P(S | C) = 7% / 15% = 0.47

So, the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars is 0.47, or 47%.

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I have no idea thank me for my help

We are given the following function

Where y is the cost of producing a computer desk and x is the number of computer desks.

Let us find the cost of producing computers for the given x number of computers.

For x = 100

For x = 200:

For x = 300:

Therefore, the complete table is

Now, let us find the number of computer desk that can be produced for $7570.

Substitute y = 7570 into the function

Therefore, 73 computer desks can be produced for $7570.

The value of cos(6A3) is 0.538.

We have,

First, we need to find the power series expansion of (2n+1) \(tan^{-1}x:\)

\((2n+1)tan^{-1}x = \sum(-1)^n x^{2n+1} / (2n+1)\)

We need to evaluate the relative percent truncation errors A1, A3, and A5 at x = √2 - 1, which means we need to substitute this value into the power series expansion and calculate the corresponding En and An.

At n = 1, we have:

\((2n+1) tan^{-1}x = 2 tan^-{1} x = 2 \times (1/8) = 1/4\)

\((2n+1)tan^{-1}x\)evaluated at x = √2 - 1 is:

2(√2 - 1) = 2√2 - 2

The power series expansion of \((2n+1) tan^{-1}x\) up to n = 1 is:

\(2 tan^{-1}x = x - x^3/3\)

Substituting x = √2 - 1, we get:

2(√2 - 1) ≈ (√2 - 1) - (√2 - 1)³/3

Simplifying, we get:

2√2 - 2 ≈ (√2 - 1) - (4√2 - 6 + 3) / 3

2√2 - 2 ≈ -5√2/3 + 5/3

So the truncation error, E1, is:

E1 = (2√2 - 2) - (-5√2/3 + 5/3) = 11√2/3 - 7/3

The relative percent truncation error, A1, is:

A1 = |E1 / (2√2 - 2)| * 100 ≈ 0.381%

At n = 3, we have:

\((2n+1) tan^{-1}x = 8 tan^{-1}x = 1\)

\((2n+1) tan^{-1}x\)evaluated at x = √2 - 1 is:

8(√2 - 1) = 8√2 - 8

The power series expansion of \((2n+1) tan^{-1}x\) up to n = 3 is:

\(2 tan^{-1}(x) + 2/3 tan^{-1}(x)^3 = x - x^3/3 + 2/3 x^5/5 - 2/5 x^7/7\)

Substituting x = √2 - 1, we get:

\(8√2 - 8 ≈ (√2 - 1) - (√2 - 1)^3/3 + 2/3 (√2 - 1)^5/5 - 2/5 (√2 - 1)^7/7\)

Simplifying, we get:

8√2 - 8 ≈ -106√2/105 + 26/35

So the truncation error, E3, is:

E3 = (8√2 - 8) - (-106√2/105 + 26/35) = 806√2/105 - 86/35

The relative percent truncation error, A3, is:

A3 = |E3 / (8√2 - 8)| x 100 ≈ 0.378%

At n = 5, we have:

\((2n+1) tan^{-1}(x) = 32 tan^{-1}(x) = 32(1/8) = 4\)

\((2n+1) tan^{-1}(x)\) evaluated at x = √2 - 1 is:

32(√2 - 1) = 32√2 - 32

The power series expansion of 2n+1 tan^-1(x) up to n = 5 is:

\(2 tan^{-1}(x) + 2/3 tan^{-1}(x)^3 + 2/5 tan^{-1}(x)^5\)

\(= x - x^3/3 + 2/3 x^5/5 - 2/5 x^7/7 + 2/7 x^9/9 - 2/9 x^11/11\)

Substituting x = √2 - 1, we get:

\(32\sqrt2 - 32 = (\sqrt2 - 1) - (\sqrt2 - 1)^3/3 + 2/3 (\sqrt2 - 1)^5/5 - 2/5 (\sqrt2 - 1)^7/7 + 2/7 (\sqrt2 - 1)^9/9 - 2/9 (\sqrt2 - 1)^{11}/11\)

Simplifying, we get:

32√2 - 32 ≈ -682√2/693 + 238√2/231 - 44/77

So the truncation error, E5, is:

E5 = (32√2 - 32) - (-682√2/693 + 238√2/231 - 44/77)

= 10852√2/693 - 5044√2/231 + 2508/77

The relative percent truncation error, A5, is:

A5 = |E5 / (32√2 - 32)| x 100 ≈ 0.376%

Finally, we need to calculate cos(6A3):

cos(6A3) = cos(6 x ln(A3)) = cos(ln(A3^6)) = A3^6

Substituting the value of A3, we get:

A3^6 ≈ 1.001149

So, cos(6A3) is approximately 0.538.

Therefore,

The value of cos(6A3) is 0.538.

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Answer:

the graph shift down 135 units

Step-by-step explanation:

when there is no fixing cost:

f(x)=12x-1400

when there is fixing cost (0ne time): 12x-(1400+135)

the graph shift down 135 units

hope this helps!

Answer: 53

Step-by-step explanation:

This last occurred in the year 2016 and will occur again in 2044.

Answer:

Step-by-step explanation:

\(y = 11x + 11b\\Move \: 11x\:to\:the \:left\:and\:change\:its\:sign\\\\y -11x =11b\\\\Divide\:both\:sides\:of\:the\:equation\:by\: 11\\\frac{y}{11} -\frac{11x}{11} = \frac{11b}{11} \\y/11 -x =b\\\\b = \frac{y}{11} - x\)

Answer: b = y/11 - x

Step-by-step explanation: You have to isolate your variable by dividing each side of the equation by your factors that DO NOT contain any variable.

I hope this helps you out.

The length of sides BC and XC in the triangle are 8.66 and 10 units respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

From the triangle shown, using trigonometric ratio:

sin(30) = 5/XC

XC = 10

Also:

tan(30) = 5/BC

BC = 8.66

The length of BC and XC are 8.66 and 10 units respectively

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1. Statement: True

Inverse: True

Contrapositive: True

Converse: True

2. Statement: True

Inverse: True

Contrapositive: True

Converse: True

3. Statement: True

Inverse: True

Contrapositive: True

Converse: True

(i)

Statement: If the difference x - y is even, then x and y are also even.

Inverse: If x and y are not even, then the difference x - y is not even.

Contrapositive: If x and y are not even, then the difference x - y is not even.

Converse: If x and y are even, then the difference x - y is even.

Statement: If a divides b or a divides c, then a divides bc.

Inverse: If a does not divide b and a does not divide c, then a does not divide bc.

Contrapositive: If a does not divide b and a does not divide c, then a does not divide bc.

Converse: If a divides bc, then a divides b or a divides c.

Statement: If x^2 ≥ 100 and x ≥ 0, then x ≥ 10.

Inverse: If x^2 < 100 or x < 0, then x < 10.

Contrapositive: If x^2 < 100 or x < 0, then x < 10.

Converse: If x ≥ 10, then x^2 ≥ 100.

(ii)

For each statement, we need to evaluate the truth values of the statement, inverse, contrapositive, and converse.

Statement: True

Inverse: True

Contrapositive: True

Converse: True

Statement: True

Inverse: True

Contrapositive: True

Converse: True

Statement: True

Inverse: True

Contrapositive: True

Converse: True

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Answer:

7/10

(-4×-7)/(5×8)

=28/40

=7/10

Answer:

c

Step-by-step explanation:

because ist winning one

The given events are independent  because choosing one a $25 winner won't affect a $50 winner, and viceversa.

Remember that two events are independent if they don't influence each other. So , in this case, once they choose the first entry, they replace it back, restoring the pool to its original size.

Hence , the answer is independent events.

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