What is an equation of the line that passes through the points (3, 3) and
(3, -3)?

We will simplify the left hand side of the equation to look like the right

\(\displaystyle \frac{1-sin(t)}{cos^{2}(t)} + \frac{1}{1 - sin(t)}\)

taking the LCM

\(\displaystyle \frac{[1-sin(t)]^{2} + cos^{2}(t)}{[cos^{2}(t)][1 - sin(t)]}\)

expanding the binomial in the numerator

\(\displaystyle \frac{[1 + sin^{2}(t) - 2sin(t) + cos^{2}(t)]}{[cos^{2}(t)][1 - sin(t)]}\)

Since sin²x + cos²x = 1

\(\displaystyle \frac{[2 - 2sin(t)]}{[cos^{2}(t)][1 - sin(t)]}\)

factoring out the 2 from the numerator

\(\displaystyle \frac{2[1 - sin(t)]}{[cos^{2}(t)][1 - sin(t)]}\)

1-sin(t) will cancel out

\(\displaystyle \frac{2}{cos^{2}(t)}\)

since cos²(t) = 1/(sec²(t))

\(2 sec^{2}(t)\)

which is equal to the right hand side of our given equation.

So we verified the identity!

Answer:

\(\rm 2 \sec {}^{2} T\)(Verified identity)

Step-by-step explanation:

Please refer to the attachment for calculations.

I hope this helps!

The nurse will have to administer 3 milliliters with each dose.

When the prescriber orders medication f 150 mcg po q.12h, the pharmacy sends a bottle labeled:

medication f 0.05 mg/ml.

Milliliters will the nurse administer with each dose :

The conversion factor from mcg to mg is 1/1000.

Therefore, 150 mcg = 150/1000 = 0.15 mg.

The nurse has to administer 0.15 mg of medication f per dose.

The medication f available with the pharmacy is 0.05 mg/ml.

So, the nurse has to administer 0.15 mg in a single dose, which is equal to three times the quantity of medication f available in the bottle (0.05 mg/ml).

Therefore, the nurse has to administer 3 ml (0.05 mg/ml × 3 ml) of medication f with each dose.

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Answer:

Please check the explanation.

Step-by-step explanation:

1) Writing the equation of the pattern

Figure 1 has 4 circles.

Figure 2 has 7 circles.

Figure 3 has 10 circles.

Thus, the sequence becomes

4, 7, 10,...

Finding the common difference between the adjacent terms

d = 7 - 4 = 3, d = 10 - 7 = 3

As the common difference is the same, so this represents the Arithmetic sequence.

so

d = 3

as

a₁ = 4

Thus, the nth term of the Arithmetic sequnce is

aₙ = a₁ + (n-1)d

aₙ = 4 + (n-1)3

aₙ = 4 + 3n - 3

aₙ = 1 + 3n

2) Determining the circles in the 23rd figure

As the nth term is given by

aₙ = 1 + 3n

putting n = 23

a₂₃ = 1 + 3(23)

a₂₃ = 1 + 69

a₂₃  = 70

3) Determining the figure having 82 circles

As the nth term is given by

aₙ = 1 + 3n

Given

aₙ = 82

To determine

n=?

Thus,

aₙ = 1 + 3n

82 = 1 + 3n

3n = 82-1

3n = 81

Dividing both sides by 3

n = 27

Therefore, 27th figure will have 82 circles.

The greatest possible number of different types of this caterpillar that could exist is 120.

If we assume that the order of the parts does not matter and that all caterpillars with the same color arrangement are considered identical, we can use combinations to find the number of different types of caterpillars that could exist.

First, we need to choose 2 out of the 5 parts to be green, which can be done in 5 choose 2 ways:

5 choose 2 = (5!)/(2!(5-2)!) = 10

For each green-yellow arrangement there are;

3! ways to permute the yellow parts and

2! ways to permute the green parts.

Therefore, the total number of different types of caterpillars is:

10 × 3! × 2! = 10 × 6 × 2 = 120

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Answer:

10cm 5cm is on top

10cm 20cm is in middle

10cm 30cm is on bottom

Step-by-step explanation:

Answer:

118.0

Step-by-step explanation:

using Trigonometry,

\(x = 99tan(50) \\ = 118.0\)

One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).

By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.

This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.

Option B holds true.

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The factors that affect the width of a confidence interval are a. population variation, c. sample size, and d. confidence level

Confidence interval refers to a statistical measure that attempts to estimate the range of values that could plausibly contain the true value of a population parameter. A confidence interval, in other words, is a statistical range that tells us how sure we are that a statistical estimate we're interested in lies between two values.

There are several factors that can affect the width of a confidence interval. Here are some of them:

The Question was Incomplete, Find the full content below :

what factors of the following affect the width of a confidence interval?

a. population variation

b. none of them

c. sample size

d. confidence level

e. sample mean

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Answer:

Step-by-step explanation:

100 +  100 + 6x + 6 + 12x - 8 = 360        Equation. Collect like terms.

198 + 18x = 360                                       Subtract 198 from both sides

18x = 360 - 198

18x = 162                                                 Divide by 18

x = 162/18

x = 9

c. incremental model Agile methods are iterative and incremental approaches to software development that prioritize customer satisfaction through the early and continuous delivery of working software.

The incremental model is a key aspect of agile methods, where the software is developed incrementally through a series of iterations or sprints. At the end of each iteration, user feedback is collected and incorporated into the next iteration, allowing the software to evolve and adapt to changing requirements. This approach allows for greater flexibility and responsiveness to user needs and helps ensure that the final product meets customer expectations.

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To solve this problem we need to first find the time it takes for the compressor to fill one tire. This is done by dividing the total time by the total number of tires filled in that time.

It takes 1.03 seconds per tire. If we need to fill 3 tires we will have to multiply the time it takes to fill one by 3.

It'd take 3.09 s.

Answer:

16/81

Step-by-step explanation:

2/3 x 2/3 x 2/3 x 2/3

4/9 x 2/3 x 2/3

8/27 x 2/3

16/81

Answer:

its team 1

i got it right

plz give me 55 points

Step-by-step explanation:

The equivalent solution to the expression (15³)(15-7) is 27000.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is (15³)(15-7). The expression will be solved as below:-

E = (15³)(15-7).

E = 3375 x 8

E = 27000

Therefore, the solution of the expression is 27000.

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Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

Answer:

you just do T-minus 5 4 3 2 1 and then T-plus 5 4 3 2 1

Answer:

between 10 and 22

Step-by-step explanation:

A side of a triangle must measure between the difference of the lengths of the other two sides and the sum of the lengths of the other two sides.

Difference: 16 - 6 = 10

Sum: 6 + 16 = 22

Answer: between 10 and 22

The length of the third side of the triangle is 2x+13.

According to the question,

We have the following information:

A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.

We know that perimeter of triangle is the sum of all three sides of triangle.

Let's take its third side to be y.

So, we have the following expression:

3x+2x-5+y = 7x+8

5x-5+y = 7x+8

Adding 5 on both the sides:

5x+y = 7x+8+5

5x+y = 7x+13

Subtracting 5x from both the sides:

y = 7x-5x+13

y = 2x+13

Hence, the correct option is B.

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Answer:

B. 2x+13

Step-by-step explanation:

I got it right on the test

Answer:

Step-by-step explanation:

Third angle = 180 - (40 + 60)

                   = 180 - 100

                   =  80°

When you subtract the sum of 40 and 60 from 180, you will get the third angle.

a) The number of units that produces maximum profit is: q = 11/6.

b) The price per unit that produces maximum profit is: p = 36.

c) The maximum profit is P = -698/9.

The cost and profit functions are given as:

C(q) = 80 + 14q

p = 58 - 12q

To find the number of units that produces maximum profit, we need to find the value of q that maximizes the profit function.

The profit function, P(q), is given by:

P(q) = Revenue - Cost

The revenue is given by:

Revenue = Price * Quantity

R(q) = p * q

The cost is given by:

Cost = Fixed Cost + Variable Cost

C(q) = 80 + 14q

Substituting the given price equation p = 58 - 12q into the revenue equation, we get:

R(q) = (58 - 12q) * q

Now we can express the profit function in terms of q:

P(q) = R(q) - C(q)

P(q) = (58 - 12q) * q - (80 + 14q)

P(q) = 58q - 12q² - 80 - 14q

P(q) = -12q² + 44q - 80

a) To find the number of units that produces maximum profit, we need to find the value of q that maximizes the profit function P(q). This can be done by taking the derivative of P(q) with respect to q and setting it equal to zero.

P'(q) = -24q + 44

-24q + 44 = 0

-24q = -44

q = 44/24

q = 11/6

So, the number of units that produces maximum profit is q = 11/6.

b) To find the price per unit that produces maximum profit, we can substitute the value of q = 11/6 into the price equation p = 58 - 12q:

p = 58 - 12 * (11/6)

p = 58 - 22

p = 36

So, the price per unit that produces maximum profit is p = 36.

c) Finally, to find the maximum profit, we can substitute the value of q = 11/6 into the profit function P(q):

P(q) = -12 * (11/6)² + 44 * (11/6) - 80

Simplifying the expression, we get:

P(q) = 88/3 - 484/18 - 80

P(q) = 88/3 - 242/9 - 80

P(q) = (264 - 242 - 720)/9

P(q) = -698/9

So, the maximum profit is P = -698/9.

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Answer:

good for Kristen! lol

Step-by-step explanation:

glad she's enjoying herself! thanks for the points... have a good day!

Answer:

yrsese

Step-by-step explanation:

Answer:

z, y and x

Step-by-step explanation:

Now, to answer this question, what we must know is that the side facing the largest angle is the largest while the side facing the smallest is the smallest.

What i’m saying in essence is that the bigger the angle faced, the larger the side.

Now since we have 3 angles in a triangle that adds up to 180

we have 27 and 48 already, the third side would be 180-27-48 = 105

So which side faces which angle?

Let’s have a diagrammatic representation of the said triangle.

Check this in the attachment please

The longest side is thus z, followed by y and lastly x

The measure of the angle from shortest to longest will be ∠z, ∠y, and ∠x.

An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).

Given data;

m∠X = 27°

m∠Y = 48°

The sum of the angle of the triangle is 180°

m∠X+m∠Y+m∠Z = 180°

27° +48° + m∠Z  =  180°

m∠Z = 105°

The order of the angle measurement;

m∠Z > m∠Y > m∠X

Hence, the measure of the angle from shortest to longest will be ∠z, ∠y, and ∠x.

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Answer:

(x-4)^2 + (y+5)^2 = 324

Step-by-step explanation:

The equation of a circle is given by the equation (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center point of the circle.

Therefore, since the center point of the circle and the radius is given, we can just plug the numbers into the formula:

(x-4)^2 + (y+5)^2 = 18^2

(x-4)^2 + (y+5)^2 = 324

The range of k for real roots is k ≥ 0.

For the characteristic equation s^2 + 4s + k = 0, the range of k should be greater than or equal to zero to ensure all the roots are real.

The characteristic equation of a control system is given as s^2 + 4s + k = 0, where s represents the complex variable and k is a constant term. To have real roots, the discriminant of the equation (b^2 - 4ac) must be greater than or equal to zero. In this case, the discriminant is 4^2 - 4(1)(k) = 16 - 4k. For real roots, this should be greater than or equal to zero. Solving the inequality 16 - 4k ≥ 0, we find k ≤ 4. Therefore, the range of k for real roots is k ≥ 0.

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Answer:

The total area codes that are currently available is 692.

Step-by-step explanation:

The area code is of the form: NXX.

The variable N can take values,

N = {2, 3, 4, 5, 7, 8 and 9}

The variable X can take values,

X = {0, 1, 2, 3, 4, 5, 7, 8 and 9}

Considering that repetitions are allowed.

The total possible number of area codes is:

T = 8 × 10 × 10 = 800

So, there are 800 possible area codes.

The exception codes are:

{37X, 96X, N9X and N11}

So, the number of reserved area codes is, 10 + 10 + 80 + 8 = 108.

Then the area codes that are currently available is, 800 - 108 = 692

Thus, the total area codes that are currently available is 692.

The solution to the system of equations is:

x = 1 ,y = -2 and z = 2

To solve the system of equations:

2x + 3y - z = 2 ---(1)

-6x - 4y - 4z = -12 ---(2)

3x - 3y + 10z = 10 ---(3)

We can use the method of elimination or substitution to find the values of x, y, and z that satisfy all three equations simultaneously.

Method of Elimination:

Multiply equation (1) by 2 and equation (2) by 3:

4x + 6y - 2z = 4 ---(4)

-18x - 12y - 12z = -36 ---(5)

Add equations (4) and (5) together:

-14x - 6y - 14z = -32 ---(6)

Multiply equation (3) by 2:

6x - 6y + 20z = 20 ---(7)

Add equations (6) and (7) together:

-14x + 14z = -12 ---(8)

Solve equation (8) for x:

-14x = -12 - 14z

x = (-12 - 14z)/(-14)

x = (6 + 7z)/7 ---(9)

Substitute the value of x from equation (9) into equation (1):

2((6 + 7z)/7) + 3y - z = 2

(12 + 14z)/7 + 3y - z = 2

12 + 14z + 21y - 7z = 14

21y + 7z = 2 ---(10)

Multiply equation (3) by 2:

6x - 6y + 20z = 20 ---(11)

Substitute the value of x from equation (9) into equation (11):

6((6 + 7z)/7) - 6y + 20z = 20

(36 + 42z)/7 - 6y + 20z = 20

36 + 42z - 42y + 140z = 140

42z - 42y + 182z = 104

42z + 182z - 42y = 104

224z - 42y = 104 ---(12)

Solve equations (10) and (12) simultaneously to find the values of y and z.

Once the values of y and z are determined, substitute them back into equation (9) to find the value of x.

Therefore, the solution to the system of equations is x = 1, y = -2, and      z = 2.

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