Let (2, -3) be a point on the terminal side of 0. Find the exact values of sin 0, sec 0, and tan 0. 0/0 sin 0 = Ú Ś sec 0 = 0 tan 0 = X ?

Answer:

x = 3 for the point of intersection of these two lines

Step-by-step explanation:

Please, label these functions:  y = 2x + 3 and y = 4x - 3.

Solve this system by equating the left function to the right one:

2x + 3 = 4x - 3

Combining like terms results in:

6 = 2x

Therefore, x = 3 for the point of intersection of these two lines.

To find the probability of A∩B, we can use the conditional probability formula where we get 0.55.

The formula is as follows:

Pr(A∩B) = Pr(B|A) * Pr(A)

We are given:
Pr(A) = 12/36
Pr(B|A) = 4/24

Now, we plug the values into the formula:

Pr(A∩B) = (4/24) * (12/36)

First, simplify the fractions:
Pr(A) = 12/36 = 1/3
Pr(B|A) = 4/24 = 1/6

Now, multiply the simplified fractions:
Pr(A∩B) = (1/6) * (1/3)

Pr(A∩B) = 1/18

To express the answer to three decimal places, we convert the fraction to a decimal:

1 ÷ 18 ≈ 0.0556

The first three decimal places are 0.055, so our answer is:

Pr(A∩B) = 0.055

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Answer: 32 miles

Step-by-step explanation:

48-16

48

-16

__

32

To find the percentage of time that cars will be unable to enter the queue, we need to use the M/M/1 queueing model with finite queue length. The M/M/1 model assumes that the arrival and service times are both exponentially distributed, which is the case in this problem. The finite queue length means that there is a limit to the number of cars that can be in the waiting line.

The parameters for this model are:

λ = 20 cars per hour = 0.333 cars per minute (arrival rate)
μ = 1 car per 2 minutes = 0.5 cars per minute (service rate)
K = 3 (maximum queue length)

The probability that the queue is full and a car cannot enter is given by the formula:

P(K) = (1 - ρ) * (ρ^(K+1)) / (1 - ρ^(K+1))

where ρ = λ / μ is the traffic intensity.

Plugging in the values for λ, μ, and K, we get:

ρ = 0.333 / 0.5 = 0.666
P(3) = (1 - 0.666) * (0.666^(3+1)) / (1 - 0.666^(3+1))
P(3) = 0.334 * 0.197 / (1 - 0.197)
P(3) = 0.0658

Therefore, the percentage of time that cars will be unable to enter the queue is 6.58%.

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Answer:

x=7 and y=19

Step-by-step explanation:

20x+8y=292

15x+8y=257

subtract everything in order to eliminate 8y

5x=35

x=7

substitute

20(7)+8y=292

8y=152

y=19

Answer:

(0,-5)

Step-by-step explanation:

First you want to simplify this equation by distributing the 3 into x-4:

y+9 = -3x+4

Next subtract 9 from both sides:

y= -3x -5

Now since I am assuming you want the Y-Intercept because you didn't ask for a specific point then it passes through the Y axis at the point (0,-5)

Answer:

i think its a or d

Step-by-step explanation:

When comparing variables x and y that are in the list '(AB), the comparison function we use is EQ.

Here's an explanation:

In Lisp, the EQ operator compares whether the two arguments are the same memory location.

EQV, on the other hand, checks whether the two values being compared are equivalent to each other.

For example, EQV will return true for two identical strings, while EQ will not.

The comparison function that should be used to compare variables x and y, which are both in the list '(AB), is EQ.

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1) El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

1) En este problema tenemos el caso de un vehículo que se desplaza a rapidez constante. Aquí tenemos que la rapidez (v), en kilómetros por hora, es inversamente proporcional al tiempo invertido (t), en minutos.

[(40 km /h) / (50 km / h)] = t / 20 min

4 / 5 = t / 20

t = 80 / 5

t = 14 min

El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) El porcentaje correspondiente a la rapidez reportada se calcula mediante porcentajes:

r = [(50 km / h) / (90 km / h)] × 100 %

r = 55.556 %

La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

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The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.

Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%

In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:

The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.

The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation

Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.

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(a) The formula for A(t), the balance after t years = 4000 * e^(0.055t)

(b) The differential equation satisfied by A(t) is dA/dt = r * A(t)

(c) The balance after 2 years is approximately $4531.16

(d) The balance will reach $8000 after approximately 12.62 years.

(e) The balance is growing at a rate of approximately $440 per year when it reaches $8000.

(a) The formula for A(t), the balance after t years, in a continuously compounded interest scenario can be given by:

A(t) = P * e^(rt)

where A(t) is the balance after t years, P is the initial deposit (principal), r is the interest rate, and e is the base of the natural logarithm.

In this case, P = $4000 and r = 5.5% = 0.055.

Therefore A(t) = 4000 * e^(0.055t)

(b) The differential equation satisfied by A(t) can be obtained by taking the derivative of A(t) with respect to t:

dA/dt = P * r * e^(rt)

Since r is constant, we can simplify it further:

dA/dt = r * A(t)

(c) To obtain the balance after 2 years, we can substitute t = 2 into the formula for A(t):

A(2) = 4000 * e^(0.055 * 2) ≈ $4531.16

Therefore, the balance after 2 years is approximately $4531.16.

(d) To obtain when the balance reaches $8000, we can set A(t) equal to $8000 and solve for t:

8000 = 4000 * e^(0.055t)

Dividing both sides by 4000 and taking the natural logarithm of both sides, we get:

ln(2) = 0.055t

∴ t = ln(2) / 0.055 ≈ 12.62 years

Therefore, the balance will reach $8000 after approximately 12.62 years.

(e) To obtain how fast the balance is growing when it reaches $8000, we can take the derivative of A(t) with respect to t and evaluate it at t = 12.62:

dA/dt = r * A(t)

dA/dt = 0.055 * A(12.62)

Substituting the value of A(12.62) as $8000:

dA/dt ≈ 0.055 * 8000 ≈ $440 per year

Therefore, the balance is growing at a rate of approximately $440 per year when it reaches $8000.

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Answer:

The volume is 1436.8\(in^2\) .

Step-by-step explanation:

-To find the volume of a sphere, you need the formula:

\(V = \frac{4}{3} \pi r^3\)

-Use the radius for the formula:

\(V = \frac{4}{3} \pi 7^3\)

-Then, you solve:

\(V = \frac{4}{3} \pi 7^3\)

\(V = \frac{4}{3}\) × \(\pi\) × \(7^3\)

\(V = \frac{4}{3} \pi\) × \(343\)

\(V = \frac{1372}{3} \pi = 1436.755\)

-Round the answer to the nearest tenth:

\(V = 1436.8\)

So, therefore the volume is 1436.8\(in^2\) .

Answer:

The volume is 1436.8 .

Step-by-step explanation:

-To find the volume of a sphere, you need the formula:

-Use the radius for the formula:

-Then, you solve:

×  ×

×

-Round the answer to the nearest tenth:

So, therefore the volume is 1436.8

Answer:

the answer would be 120 square yards

Step-by-step explanation:

you multiply the 15 and 24 then after that you divide the out come by 3 because a square yard is 3 by 3

Answer: y=8x+6

Step-by-step explanation:

The slope is

\(\frac{70-54}{8-6}=\frac{16}{2}=8\)

So, the slope is 8.

Since the y-intercept is 6, the equation is y=8x+6.

Answer:

64 degrees

Step-by-step explanation:

since it is in between the both of them and they both share the 62 degree angle

Answer:

180°

Step-by-step explanation:

Step-by-step explanation:

10% per hour is tricky, because for the first hour it is 10% of the original 140 mg (14 mg). but for the second hour it is 10% of the updated level of 140 - 14 = 126 mg (12.6 mg). and so on.

so, we cannot simply say 5× 10% = 50%, therefore, it will take 5 hours.

no, instead we must use arithmetic sequences.

10% is represented as mathematical factor as 0.1.

so, when 10% are removed, it means that 90% remain.

90% = 0.9.

90% of 100% = 100% × 0.9

so,

a1 = 140

a2 = a1×0.9

a3 = a2×0.9 = a1×0.9²

an = a1×0.9^(n-1)

we need to find n for which an = 70 (half of the caffeine remains, meaning half of the caffeine is gone).

70 = 140×0.9^(n-1)

0.5 = 0.9^(n-1)

using the logarithm to the base of 0.9 to solve :

log0.9(0.5) = n - 1

n = log0.9(0.5) + 1

how to get log0.9(0.5) ?

all logarithms are related to each other :

loga(b) = logc(b)/logc(a)

in our case we can use ln (base e) or log (base 10) - whatever your calculator offers :

log0.9(0.5) = log(0.5)/log(0.9) = 6.578813479...

n = 6.578813479... + 1 = 7.578813479... hours

0.578813479...×60 = 34.72880874... minutes

so, after about 7.6 hours or 7 hours and 35 minutes half of the caffeine will be gone.

Answer:

The Total Surface Area of cone is 264 cm²

Step-by-step explanation:

Radius (r) = 6 cm

Slant height (l) = 8 cm

To find TSA of cone

A = πr(l + r)

A = 22/7 × 6 × (8 + 6)

A = 22/7 × 6 × (14)

A = 22/7 × 84

A = 22 × 12

A = 264 cm²

Thus, The Total Surface Area of cone is 264 cm²

-TheUnknownScientist 72

SOLUTION

Given the question in the question tab, the following are the solution steps to determine the probability.

Determine the probability of getting jack of heart and the queen of heart with replacement

Step 1: State the formula for finding the probability

Step 2: Calculate the probability with replacement

Answer:

C

Step-by-step explanation:

Answer:

C. 9x^2y^3√2xy^2

Step-by-step explanation:

I had to do this for plato, and it was marked right (at least for me).

Answer:

Katrina = 0.8

Susan = 0.833

Gabrielle = 0.85

Savannah = 0.9

Step-by-step explanation:

Change to decimal

Gabrielle = 85%

= 85/100

= 17/20

= 0.85

Savannah = 0.9

= 9/10

= 0.9

Katrina = 4/5

= 0.8

Susan = 5/6

= 0.833

Arrange from least to greatest

Katrina = 0.8

Susan = 0.833

Gabrielle = 0.85

Savannah = 0.9

Answer:

Option (D)

Step-by-step explanation:

Coordinates of the points J, E and V are,

J → (-4, -5)

E → (-4, -3)

V → (-1, -1)

This triangle is translated by the rule \(T_{<2,4>}\) given in the question.

Coordinates of the image will follow the rule,

(x, y) → [(x + 2), (y + 4)]

following this rule coordinates of the image triangle will be,

J(-4, 5) → J'(-2, -1)

E(-4, -3) → E'(-2, 1)

V(-1, -1) → V'(1, 3)

Therefore, points given in the option (D) will be the answer.

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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The calculated price is -1558. However, since prices cannot be negative in most real-world scenarios, we need to consider the valid range of prices. None of the options are correct.

To find the price at which sales are equal to Q=10, we need to substitute Q=10 into the inverse demand function P=342-190 and solve for P.

Let's start by substituting Q=10 into the inverse demand function:

P = 342 - 190 * Q

P = 342 - 190 * 10

P = 342 - 1900

P = -1558

The calculated price is -1558. However, since prices cannot be negative in most real-world scenarios, we need to consider the valid range of prices.

Given the options provided (a, 18; b, 36; c, 152; d, 171), we can see that none of them match the calculated price of -1558.

Therefore, none of the options are correct.

It is important to note that the calculated price of -1558 may not be realistic or feasible in the context of the problem. It is possible that there may be some error or inconsistency in the information provided.

If you have any additional information or if there are any constraints or limitations mentioned in the problem, please provide them, and I will be happy to assist you further.

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Answer:

0.24

Step-by-step explanation:

Total = 500

8th Grade, Fruit Smoothie = 120

120 ÷ 500 = 0.24

= 0.24

Answer:

\(32\:\mathrm{m^2}\)

Step-by-step explanation:

When cut by a diagonal, the parallelogram will be divided into two congruent triangles. By definition, congruent polygons have equal areas. Therefore, let the area of each of the triangle be \(x\):

\(x+x=64,\\2x=64,\\x=\frac{64}{2}=\boxed{32\:\mathrm{m^2}}\)

To find p(1.47 ≤ z ≤ 2.11), you need to use a standard normal distribution table or a calculator that can compute the cumulative distribution function (cdf) of the standard normal distribution.

The formula for calculating the z-score is shown below.
z = (x - μ) / σ
where x is the value you're interested in, μ is the mean, and σ is the standard deviation. In this case, we're given z-values of 1.47 and 2.11. So, to find the probability, we need to find the area under the standard normal curve between these two z-scores.

We have the given values of z as 1.47 and 2.11, We need to find the probability p(1.47 ≤ z ≤ 2.11).The following steps can be taken to solve the given problem:
Step 1: We need to find the cumulative probability at 2.11 and 1.47 using the z-table.
P(z ≤ 2.11) = 0.9838P(z ≤ 1.47) = 0.9292
Step 2: Subtract the smaller cumulative probability from the larger cumulative probability.
P(1.47 ≤ z ≤ 2.11) = P(z ≤ 2.11) - P(z ≤ 1.47)
P(1.47 ≤ z ≤ 2.11) = 0.9838 - 0.9292
P(1.47 ≤ z ≤ 2.11) = 0.0546
Therefore, the probability of P(1.47 ≤ z ≤ 2.11) is 0.0546, which is rounded to 4 decimal places, and this is the final answer.

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