Marcus dives from the surface of the ocean to a reef 18 meters below sea level. What integer represents Marcus's location relative to the surface? How far does Marcus have to go to return to the surface?

The maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.

To find the maximum and minimum values of the function y = sin x + sin 2x, we can first take its derivative with respect to x:

y' = cos x + 2 cos 2x

Then, we can set y' equal to zero and solve for x:

cos x + 2 cos 2x = 0

We can use a graphing calculator to find the solutions to this equation, which are approximately x = 0.285 and x = 2.857. We can then evaluate the original function at these values to find the maximum and minimum values:

y(0.285) ≈ 1.724

y(2.857) ≈ -1.724

Therefore, the maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.

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Answer:

Oppositeleg

adjacenleg

Answer:

option 1

Step-by-step explanation:

Just remember this to get the trigonometric ratio in a right triangle :

    Old Henry And His Old Aunt

O for opposite

H for hypotenuse

A for Adjacent

Sin = O/ H

Cos = A /H

Tan = O /A

Answer:

(2,0)

Step-by-step explanation:

-hope it helps

Answer:

the answer is 5 degrees

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Because 6+6.25=12.25  48.25-12.25=36 6x6=36 6+1=7

Answer:

found the x

it is sideways

it is 10x2

Step-by-step explanation:

2x + 1

89°

and 10x2

Given:

Find: f(-2)

Explanation:

put x=-2 in the given equation.

Final answer: the required answer is

The uncertainty in the best estimate for the length of the side of the block is approximately 0.0447 mm.

To determine the uncertainty in the best estimate for the length of the block side, we can consider the range of values obtained from the measurements. Since the uncertainty represents the possible deviation from the true value, the range of measurements can be used to estimate the uncertainty in the best estimate

To find the standard deviation represents the average amount of variation or spread among the measurements , we use the formula σ = Δb / √n, where σ is the standard deviation, Δb is the uncertainty in each measurement, and n is the number of measurements.

In this case, Δb = 0.1 mm and n = 5. Plugging these values into the formula, we get σ = 0.1 / √5 ≈ 0.0447 mm.

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Answer:

C

Step-by-step explanation:

Another power series solution of the given differential equation about the ordinary point x = 0 is simply a constant function y(x) = a₀, where a₀ is an arbitrary constant.

y'' - 4xy'y = 0.

That the answer can be written as a power series of the form: to find the power series solutions around the normal point x = 0.

y(x) = a₀ + a₁x + a₂x² + a₃x³ + ...

If x is the variable and the coefficients a₀, a₁, a₂, a₃... need to be calculated. The supplied differential equation can therefore have this expression for y(x) substituted into it, and the coefficients can then be found. To begin, let's contrast y(x) term by term:

y'(x) = a₁x + a₂x² + a₃x³ + ...

y''(x) = 2a₂ + 6a₃x + ...

The following formulas in the provided differential equation for y'(x) and y''(x):

2a₂+ 6a₃x + ... - 4x(a₁ + 2a₂x + 3a₃x² + ...)(a₁ + 2a₂x + 3a₃x² + ...) = 0.

The system of equations for the coefficients can then be obtained by equating coefficients of like powers of x on both sides of the equation.

The coefficients for the powers of x₀ and x₁ should be determined first.

For x₀ term:

2a₂ = 0, so a₂= 0.

For x^1 term:

-4a₁a₂ = 0, so a₁= 0 or a₂ = 0.

Since a₂ was expected to be zero, a₁ is arbitrary.

Let's now determine the coefficients for powers of 2x and greater.

6a₃ - 4a₁a₃- 4a²₂ = 0.

For x³ term:

0 = 0.

For x⁴ term and higher:

0 = 0.

The coefficients a₃, a₄, and higher must be arbitrary since the coefficients for powers of x of 3, 4, and higher are all equal to zero.

y(x) = a₀ + a₁x,

Let's find another power series solution. Since a₁ is arbitrary, we can set a₁ = 0 to obtain a different solution:

y(x) = a₀ .

Therefore, the constant function y(x) = a₀, where a₀ is an arbitrary constant, is another power series solution of the aforementioned differential equation about the usual point x = 0.

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The most appropriate chart to see the correlation between car mileage and year the car was built for various car models would be a scatterplot chart.

In a scatterplot chart, each point represents a pair of values: one value on the x-axis (in this case, year the car was built) and another value on the y-axis (in this case, mileage). By plotting these pairs of values for each car model in the sample, we can visually examine the relationship between mileage and year built for each car model and determine if there is a correlation between the two variables.

A line chart is used to display data that changes over time, typically for a single variable. A heatmap chart is used to show the magnitude of values for different categories using different colors. Therefore, neither of these chart types would be appropriate to show the correlation between mileage and year built for various car models.

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Answer:

Step-by-step explanation:

6 < 3x + 9 ≤ 18

~Subtract 9 to everything

-3 < 3x ≤ 9

~Divide 3 to everything

-1 < x < 3

I will assume the first drop down menu is the first valoue and the second drop down manu is the second value.

Best of Luck!

The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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To determine the angle from the vernal equinox to the station at the time of measurement, we need to use the following formula:

Angle = (Sidereal Time at Greenwich + Longitude of the Station - Hour Angle of the Object) * 15 degrees/hour

First, we need to determine the Hour Angle of the Object, which is the amount of time since the object (in this case, the radar measurement) passed over the Greenwich meridian. We know that the radar measurement occurred 2.8 hours after noon on January 1, so the Hour Angle of the Object is:

Hour Angle = 2.8 hours * 15 degrees/hour = 42 degrees

Next, we can plug in the values we know into the formula:

Angle = (100 degrees + (-4 degrees) - 42 degrees) * 15 degrees/hour
Angle = 54 degrees * 15 degrees/hour
Angle = 810 degrees/hour

Therefore, the angle from the vernal equinox to the station at the time of the radar measurement is 810 degrees/hour.

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Answer:

4

Step-by-step explanation:

To solve for x in the equation:

√(2x - 7) = 1

We can start by isolating the square root by squaring both sides of the equation:

(√(2x - 7))^2 = 1^2

2x - 7 = 1

Next, we can isolate the variable by adding 7 to both sides of the equation:

2x = 8

Finally, we can solve for x by dividing both sides by 2:

x = 4

Therefore, the solution to the equation √(2x - 7) = 1 is x = 4.

Answer:

30.5 Weeks

Step-by-step explanation:

The phone costs $930, and he already has $320 saved in his bank account so subtract 320 from 930. You will get 610. Then, you take 610 and divide it by 20 because he earns $20 a week. I hope this helped.

A , B, C are the amounts of each product

10A + 8B + 20C = 6000 <--- volume constraints

10A + 20B + 40C = 11000  <---- weight constraints

100A + 20B + 200C = 36900  <---- $$$$

Byproducts are things created in a process, typically one that is industrial or biological, in addition to the main result. A byproduct of the sugar refining process is sulfured molasses.

the first two equations together:

10A + 8B + 20C = 6000

10A + 20B + 40C = 11000

first is subtracted from second: 12B + 20C = 5000 3B + 5C = 1250 —- identifies this equation. ALPHA

Connect the second and third equations:

10A + 20B + 40C = 11000

100A + 20B + 200C = 36900

The top equation is multiplied by 10:

100A + 200B + 400C = 110000 —— Weight restrictions

100A + 20B + 200C = 36900 <—— $$$$

takes them away:

180B + 200C = 73100

18B + 20C = 7310

9B + 10C = 3655 —- identifies this equation. ALPHA BETA: BETA: 9B + 10C = 3655 3B + 5C = 1250

ALPHA is multiplied by 3:

9B + 15C = 3750

9B + 10C = 3655

takes them away:

5C = 95\s C = 95/5 = 19

Plugging into BETA yields the following results: 9B + 10(19) = 3655 9B = 3655 - 190 B = 385

Adds to the initial first equation:

10 A + 8(385) + 20(19) = 6000 A=254\s A=254\sB=385\sC=19

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Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:

x1 + x2 + x3 + 2x4 + s1 = 4,

-x1 + x3 + x4 - s2 = -1,

2x1 + x2 + s3 = 2,

and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.

To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.

The standard form of a linear programming problem is as follows:

Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4

Subject to:

a11x1 + a12x2 + a13x3 + a14x4 = b1

a21x1 + a22x2 + a23x3 + a24x4 = b2

a31x1 + a32x2 + a33x3 + a34x4 = b3

an1x1 + an2x2 + an3x3 + an4x4 = bn

x1, x2, x3, x4 >= 0

Now let's reformulate the given problem:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 <= 4

-x1 + 0x2 + x3 + x4 >= -1

2x1 + x2 + 0x3 + 0x4 <= 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4 >= 0

The reformulated linear programming problem in standard form is as follows:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 + s1 = 4

-x1 + x3 + x4 - s2 = -1

2x1 + x2 + s3 = 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4, s1, s2, s3 >= 0

Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.

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Answer:

plz explain ?

Step-by-step explanation:

There are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

For the number to be divisible by 5, its units digit must be either 0 or 5. Since we cannot repeat digits, we have two cases to consider:

Case 1: The units digit is 0.

In this case, we have 5 choices for the units digit (0, 1, 2, 3, or 4). For the remaining four digits, we can choose them in 4! ways (i.e., 4 choices for the first digit, 3 choices for the second digit, 2 choices for the third digit, and 1 choice for the fourth digit).

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 0 is:

5 × 4! = 120

Case 2: The units digit is 5.

In this case, we have only one choice for the units digit, which is 5. For the remaining four digits, we can choose them in 4! ways as before.

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 5 is:

1 × 4! = 24

The total number of ways to form a five-digit number that is divisible by 5 without repeating digits is the sum of the numbers from both cases:

120 + 24 = 144

Therefore, there are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

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Answer:

2x^3+3x^2-50x-75

Step-by-step explanation:

(x+5)(x-5)=x^2-25

(x^2-25)(2x+3)=2x^3+3x^2-50x-75

Can I have brainliest!

Answer:

b=45 c=45

Step-by-step explanation:

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

all of the above

Step-by-step explanation:

The point of portrait orientation is to make it so the picture focuses on the person. In order to do this you need to minimize the background, place attention on the foreground, and show more context

Answer:

all of the above

Step-by-step explanation:

The next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

To find the time at which all three lights will flash at the same time, we need to find the LCM (Least Common Multiple) of the given times.

Prime factorizing each time, we get:

6 = 2 x 3

15 = 3 x 5

21 = 3 x 7

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

2 x 3 x 5 x 7 = 210

Therefore, the next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

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Answer:

x=-2

Step-by-step explanation:

4(x+5)=12

Divide both sides by 4

x+5=12/4

Simplify 12/4 to 3

x+5=3

Subtract five from both sides

x=3-5

Hope this helps!

Answer:

take any two points x,y

y-11 /x-2=3/1

1(y-11)=3(x+5)

y-11=3x-6

y=3x-6+11

y=3x+5

Answer:

12.3693169

Step-by-step explanation:

x^2+y^2=r^2

(12)^2=(3)^2=sqroot(153)

=12.3693169

To determine the remaining sides and angles of triangle ABC, we are given the following information: Angle A = 130° 50' Angle C = 20° 10' Side AB = 1, Angle B comes as Angle B ≈ 29°and  BC ≈ sin(29°) / sin(130.83°) AC ≈ sin(20.17°) / sin(130.83°)

To find the remaining angles, we can use the fact that the sum of the angles in a triangle is always 180°. Thus, we can find angle B using the equation: Angle B = 180° - Angle A - Angle C Angle B = 180° - 130° 50' - 20° 10'

To calculate this, we need to convert the angles to a consistent unit. Let's convert the angles to degrees:

Angle A = 130° + (50'/60') ≈ 130.83°

Angle C = 20° + (10'/60') ≈ 20.17°

Now we can calculate angle B:

Angle B = 180° - 130.83° - 20.17°

Angle B ≈ 29°

Next, to find the remaining sides, we can use the Law of Sines. The Law of Sines and cosine states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides of a triangle. We can set up the following proportion:

AB/sin(A) = BC/sin(B) = AC/sin(C)

We know AB = 1 and angles A and C, so we can solve for BC and AC.

BC/sin(B) = 1/sin(A)

BC = sin(B) / sin(A)

AC = sin(C) / sin(A)

Using the known values, we can calculate BC and AC:

BC ≈ sin(29°) / sin(130.83°)

AC ≈ sin(20.17°) / sin(130.83°)

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Answer:

1746

Step-by-step explanation:

6/10 x 2910

= 17460/10

=1746

Answer:

1746

Step-by-step explanation:

6/10 x 2910

= 17460/10

=1746