Slope review NEED HELP ASAP

Answer: x = 5/49 ; 0.102041

Step-by-step explanation:

An acute angle theta that satisfies the equation sin θ =cos (2 theta + 27 degrees) is 45 degrees.

To find an acute angle theta that satisfies the equation sin theta =cos (2 theta + 27 degrees), we can use the identity cos (90 - theta) = sin theta.

Substituting 90 - theta for 2 theta + 27 degrees, we get:
sin theta = cos (90 - theta)

Using the identity cos (90 - theta) = sin theta, we can simplify the equation to:
sin theta = sin (90 - theta)
Since sin θ = sin (90 - theta), we can conclude that theta = 90 - theta.
Solving for theta, we get:
2 theta = 90
theta = 45 degrees
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Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

x = 5 x = 4

Step-by-step explanation:

The area of triangle JHK is 4.18 units²

A triangle is a polygon with three sides having three vertices. There are different types of triangle, we have;

The right triangle, the isosceles , equilateral triangle e.t.c.

The area of a figure is the number of unit squares that cover the surface of a closed figure.

The area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

The base = 2.2

height = 3.8

A = 1/2 × 3.8 × 2.2

A = 8.36/2

A = 4.18 units²

Therefore the area of triangle JHK is 4.18 units²

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Zane set out to create a table that would demonstrate equivalent ratios for x and y, but after completing it, he noticed an error.

As per the question given,  

Determined to correct the mistake and provide accurate information, he took a closer look at each row and column of the table to identify the incorrect number.

Using his problem-solving skills, Zane was able to pinpoint the incorrect number and replace it with the correct one, ensuring that the table accurately represented the equivalent ratios for x and y. With this correction, Zane could rest easy knowing that he had provided reliable information for others to use and reference.

As the saying goes, "to err is human," but Zane's dedication to accuracy and attention to detail ensured that his mistake did not go unnoticed, and he was able to take the necessary steps to correct it.

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At time t=2, the velocity vector is ⟨1/2, -1/4, 32⟩, the speed is sqrt(1025)/4, and the acceleration vector is ⟨-1/4, 1/2, 48⟩.

To find the velocity vector, speed, and acceleration vector of the object at time t=2, we need to take the first and second derivatives of the position vector with respect to time.

Position vector: r(t) = ⟨ln t, 1/t, t^4⟩

Velocity vector: v(t) = dr/dt = ⟨1/t, -1/t^2, 4t^3⟩

Acceleration vector: a(t) = d^2r/dt^2 = ⟨-1/t^2, 2/t^3, 12t^2⟩

To find the values at t=2, we plug in t=2 to the expressions for the velocity and acceleration vectors:

Velocity vector at t=2:

v(2) = ⟨1/2, -1/4, 32⟩

Speed at t=2:

|v(2)| = sqrt((1/2)^2 + (-1/4)^2 + 32^2) = sqrt(1025)/4

Acceleration vector at t=2:

a(2) = ⟨-1/4, 1/2, 48⟩

Therefore, at time t=2, the velocity vector is ⟨1/2, -1/4, 32⟩, the speed is sqrt(1025)/4, and the acceleration vector is ⟨-1/4, 1/2, 48⟩.

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Answer:

C

Step-by-step explanation:

1.20 dollars per kg as on the receipt and when you times 3 the amount of money, it totals 3.60

The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).

The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/\(s^2\).

To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get \(r^2\) + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.

The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).

By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.

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781.21 billion

Step-by-step explanation:

A = money 2019

P = initial amount 2004, 370 billion

r = interest 6% or 0.06

n = 15 : 2019 minus 2004

A = P(1 + r)^n

A = 370 billion (1 + 0.06)^15

A = 781.21 billion

ChatGPT

Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment: FALSE

As it is given in the description, centipedes have only one pair of legs on each body segment. So, the whole statement becomes False.

Therefore, the statement "centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment" is FALSE.

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Complete question:

Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment. TRUE or FALSE

Answer:The rate at which the tank is changing water is 2/3 gallons per minute

Step-by-step explanation:

Step 1

In 3 mins, the tank losses 7 gallons of water - 5 gallons of water

= 7- 5 = 2 gallons of water

In  3 minutes, the tank loses , 2 gallons of water

step 2

To find  rate at which amount of water is changing

if 3 minutes, tank loses 2 gallons of water.

then 1 minute the tank will lose = 2/3 gallons

Therefore rate at which tank is changing water is 2/3 gallons per minute

The conditional probability mass functions are: (a) P(X1 = 1|X3 = 1) = 2/9, (b) P(X2 = 1|X3 = 1) = 4/9, (c) P(X1 = 1|X3 = 1) = 4/14, (d) P(X2 = 1|X3 = 1) = 8/14.

(a) The conditional probability mass function given that is:

P(W1=1, W2=k | W3=j) = P(W1=1, W2=k) * P(W3=j | W1=1, W2=k) / P(W3=j)

Using Bayes' Theorem, we have:

P(W1=1, W2=k | W3=j) = (4/14) * (3/13) * (10/12) / [(4/14) * (3/13) * (10/12) + (10/14) * (4/13) * (10/12)]

Simplifying the expression, we get:

P(W1=1, W2=k | W3=j) = 6/23 if j is black and k is white, 5/46 if j is white and k is black, and 5/69 if j and k are both white.

(b) The conditional probability mass function given that is:

P(W1=k, W2=j | W3=1) = P(W1=k, W2=j) * P(W3=1 | W1=k, W2=j) / P(W3=1)

Using Bayes' Theorem, we have:

P(W1=k, W2=j | W3=1) = (4/14) * (3/13) * (10/12) / [(4/14) * (3/13) * (10/12) + (10/14) * (4/13) * (10/12)]

Simplifying the expression, we get:

P(W1=k, W2=j | W3=1) = 6/23 if k is black and j is white, 5/46 if k is white and j is black, and 5/69 if k and j are both white.

(c) The conditional probability mass function given that is:

P(W1=1, W2=k | W3=j) = P(W1=1) * P(W2=k) * P(W3=j) / (P(W1=1) * P(W2=k) * P(W3=j))

Since the balls are selected with replacement, the probability of selecting any ball is always the same. Therefore, the conditional probability mass function is the same as the joint probability mass function, which is:

P(W1=1, W2=k | W3=j) = (4/14) * (4/14) * (4/14) = 16/2744 if j, k are both white and 0 otherwise.

(d) The conditional probability mass function given that is:

P(W1=k, W2=j | W3=1) = P(W1=k) * P(W2=j) * P(W3=1) / (P(W1=k) * P(W2=j) * P(W3=1))

Since the balls are selected with replacement, the probability of selecting any ball is always the same. Therefore, the conditional probability mass function is the same as the joint probability mass function, which is:

P(W1=k, W2=j | W3=1) = (4/14) * (4/14) * (10/14) = 80/2744 if k is white and j is black, and 0 otherwise.

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It is determined if the syllogism is valid or invalid. There are four moods of categorical syllogism: A, E, I, O. A  is the arrangement of the terms in the premises and in the conclusion of the syllogism.

There are four figures possible in the categorical syllogism.3) The formal nature of the Syllogistic Argument refers to the logical form of the argument that determines its validity. Standard form allows us to determine whether the argument is valid or invalid. The standard form of the syllogism is "All A are B, all B are C, therefore all A are C."4) In the following syllogism: "All sodium salts are water-soluble substances." "All soaps are sodium salts." "Therefore, all soaps are water-soluble substances.", the subject term is "soaps," the predicate term is "water-soluble substances," and the middle term is "sodium salts."5) A syllogistic rule is used to evaluate the validity of a categorical syllogism. There are six rules to evaluate a syllogism that have to be used in order to determine the validity of a syllogism.

The fallacies committed with regard to each fallacy rule are: The Fallacy of Undistributed Middle, The Fallacy of Illicit Major, The Fallacy of Illicit Minor, The Fallacy of Exclusive , The Fallacy of Drawing an Affirmative Conclusion from a Negative Premise, The Existential Fallacy.6) The four syllogisms, the fallacies committed, and the rules broken are: EAA-1: No Men are perfect, All women are men, Therefore, No Women are perfect. The fallacy committed is Illicit Conversion. The rule broken is A rule. OAO-2: Some birds are penguins, All penguins are birds, Therefore, Some birds are not penguins. The fallacy committed is Illicit Major. The rule broken is E rule. IAA-3: Some cats are black, All cats are animals, Therefore, Some animals are black. The fallacy committed is None. The rule broken is None. EEE-1: No foods are rocks, No rocks are computers, Therefore, No computers are foods. The fallacy committed is None. The rule broken is None.

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Using Excel, the probability of having 5 initial public offerings (IPOs) in a randomly selected week can be calculated based on the given average of 2.7 IPOs per week. The result should be rounded to three decimal places.

To calculate the probability, we can use the Poisson distribution, which is often used to model the number of events occurring in a fixed interval of time. The Poisson distribution is appropriate when the events occur randomly and independently, and the average rate of occurrence is known.

In this case, the average rate of IPOs per week is 2.7. To find the probability of having 5 IPOs in a randomly selected week, we can use the POISSON.DIST function in Excel.

Using Excel, we can calculate the probability as follows:

=POISSON.DIST(5, 2.7, FALSE)

Here, the first argument is the number of IPOs (5), the second argument is the average rate (2.7), and the third argument (FALSE) indicates that we want the probability mass function value rather than the cumulative distribution function.

By evaluating this formula in Excel, we will obtain the probability of having 5 IPOs in a randomly selected week, rounded to three decimal places.

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The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Lily took a certain number, multiplied it by 3, and then subtracted 8 from the product, which resulted in 7. The initial number was 5.

The equation that describes this situation is: 3k - 8 = 7.

To solve for k, we can isolate the variable by adding 8 to both the sides of the equation:

3k - 8 + 8 = 7 + 8

3k = 15

Finally, we can solve for k by dividing both sides of the equation by 3:

k = 5

Therefore, Lily started with the number 5, tripled it to get 15, and then subtracted 8 to get an answer of 7.

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Any number out of 100 can be quickly converted to percent form by just tacking on the percent sign. This is because "percent" is "per one hundred". Think of 100 cents in a dollar which may help you remember.

So 76/100 = 76%

The number of wild bears the naturalist can relocate per month is 2 wild bears.

Number of wild bears relocated by the naturalist = 12 wild bears

Time taken by the naturalist to relocate these wild bears = 6 months

Thus the number of bears the naturalist can relocate in 1 month can be found out by using unitary method

This implies that the number of bears relocated by the naturalist in 1 month or per month = 12 / 6 = 2 wild bears

Thus the number of wild bears the naturalist can relocate per month is 2 wild bears .

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The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.

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Extra info:

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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Answer:

P = 37.4 m

Step-by-step explanation:

let the third side of the triangle be x

using Pythagoras' identity in the right triangle.

x² + 7² = 16²

x² + 49 = 256 ( subtract 49 from both sides )

x² = 207 ( take square root of both sides )

x = \(\sqrt{207}\) ≈ 14.4 m ( to 1 decimal place )

the perimeter (P) is then the sum of the 3 sides

P = 7 + 16 + 14.4 = 37.4 m

Step-by-step explanation:

m1=y2-y1/x2-x1

=-5-(-3)/-6-6

=-2/-12

=1/6

-3=1/6(6)+b

b=-4

y=1/6x-4

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:

27y^12

Step-by-step explanation:

you multiply the exponents together

in this case: 4×3=12

and then multiply the base number by 3 as well.