The elevation of a sunken ship is $-120$ feet. You are in a submarine at

an elevation that is $\frac{5}{8}$
of the ship’s elevation. What is your elevation?

Answer:

Step-by-step explanation:

Hello,

I assume that you know that

\(sin(A+B)=sinAcosB+cosAsinB\\\\sin(A-B)=sinAcosB-cosAsinB\)

One way to retrieve them quickly is to use Euler's formula and then,

\(cos(A+B)+isin(A+B)=e^{i(A+B)}=e^{iA}e^{iB}=(cosA+isinA)(cosB+isinB)\)

and you can replace B by -B for the second formula.

So, it comes that sin(A+B)-sin(A-B)=2cosAsinB

Hope this helps

Answer:

x = 14 units

Step-by-step explanation:

Answer:

The correct answer is: u = 10,500. When the value of the alternative hypothesis is greater than that of the null hypothesis, the power of the test will be increased, so a value of u = 10,500 would yield the greatest power to reject the null hypothesis.

Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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2w is the part of two factors.

The part of the expression is a product of two factors.

The expression we have is:

\(1 + \frac{z}{3}+2w\)

Let's analyze the parts of this expression.

The first term of the expression is a constant term: 1.

1 is not a product of two factors, so this is not the answer.

The second term of the expression is: z/3.

This part of the expression is a division or quotient between z and 3. Thus, since it is a division and not a product, this is also not the answer we are looking for.

The third term of the expression is: 2w

In this case, the term 2w is a product between "2" and "w". Thus, 2w is a product of two factors. The parts of this product are 2 and which when multiplied result in 2w.

Hence the answer is 2w is the part of two factors.

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Answer:

D) 2x2

Step-by-step explanation:

i got i right on the test

Answer:

2x2

\

Step-by-step explanation:

Answer:

local maximum is at (-2.5, 30)

local minimum is at (2.5, -30)

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

42

Step-by-step explanation:

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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49^2m-m : Not equivalent

7^2m-2m : Not equivalent

7^2m-m : Not equivalent

This is actually a trick question. All of the following are actually false statements. Want to know why? Let me show you.

For exponents, if you are dividing a number to some power (i.e 5^3) by the SAME number to a different power (i.e 5^2), then the expression is 5^3-2 or 5^1 = 5. This is true for any number a such that a^b ÷ a^c = a^b-c.

Since 7 and 49 are not the same number, this rule does not apply and thus cannot be simplified any further.

Let me prove why. 5^3 = 125, and 5^2 = 25, and 125 ÷ 25 = 5. This is also the same as 5^3-2 = 5^1 = 5. We just proved this as so.

But, what about 7 and 49, or 2 different numbers. Well it doesn't apply. 7^3 = 343, and 49^2 = 2401, and 343 ÷ 2401 ≈ 0.14. Thus, this is NOT equal to 7^3-2 which is 7. We just proved that a^y ÷ b^z ≠ a^y-z. Congratulations!

Hope this helped!

Answer:

x≤20

Step-by-step explanation:

x+5≤25

 -5.  -5

x≤20

Hopes this helps please mark brainliest

Answer:

The answer is B

Step-by-step explanation:

20+5=25 and x can be greater than or equal to 25

Answer: lol she was lowkey trying to call out the lady in front of you without directly addressing her. Or she was just trying to mess with you cuz that's how moms are

Step-by-step explanation:

The inverse of function f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.So, the correct option is D.

To find the inverse of a function, we switch the x and y variables and solve for y. So, if f(x) = -2, we have:
x = -2
y = f(x) = -2
Switching x and y, we get:
x = f¯¹(y)
y = -2
Solving for f¯¹(y), we get:
f¯¹(y) = 2y + 3
Therefore, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
To find the inverse of a function, we need to swap the input (x) and output (f(x)), and then solve for the new input. Given f(x) = -2, let's find the inverse:
1. Swap the input and output: x = -2
2. Solve for the new input: Since the function f(x) is a constant function and doesn't involve x, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
Therefore, Option D is the correct inverse of f(x).

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Answer:

C.

Step-by-step explanation:

So we have the equation:

\(y=\sqrt{x-3}\)

This is a square root equation.

For square root equations, the radicand(s) must be positive.

Therefore, to find the domain, set the radicand to be greater than or equal to 0:

\(x-3\geq 0\)

Solve for x. Add 3 to both sides:

\(x\geq 3\)

Therefore, our domain must be greater than or equal to 3.

In set notation, this is:

\(\{x:x\geq 3\}\)

Therefore, our answer is C.

All we need to do is solve for the 0 of the function.

Solution:

0 = √x-3

0^2 = x - 3

0 = x - 3

3 = x

The domain is greater than or equal to 3 and this can be written as x ≥ 3 or in other words, Option 3.

Best of Luck!

Answer:

x = 3 1/2.

Step-by-step explanation:

8 5/6= x + 5 1/3

x = 8 5/6 - 5 1/3

x = 8 5/6 - 5 2/6

  =   3 3/6

  =  3 1/2.

Answer:

x = 3 1/2.

8 5/6= x + 5 1/3

x = 8 5/6 - 5 1/3

x = 8 5/6 - 5 2/6

 =   3 3/6

 =  3 1/2.

Step-by-step explanation:

The correct statement is: On a coordinate plane, an absolute value graph has a vertex at (0, 1).

The function p(x) = |x - 1| represents an absolute value function. The vertex of an absolute value function in the form f(x) = |x - h| + k is given by the point (h, k). In this case, the function p(x) = |x - 1| has a vertex at (1, 0).

Therefore, none of the provided options accurately represents the vertex of the function p(x) = |x - 1|. The correct vertex for this function is (1, 0), which means the vertex is at x = 1 and y = 0 on the coordinate plane. It is important to note that the vertex is located at (h, k) where h represents the x-coordinate and k represents the y-coordinate.

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Simply put, cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.

Cultural identity can be defined as the self-perception of an individual which gives them a sense of belonging to an identical group that shares same qualities which may included music, food, traditions, social class, beliefs, ethnicity, among others.

In summary, we can say that cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.

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Answer:

Exact Form: x=11/2

Decimal Form: x=5.5

Mixed Number From: x= 1 1/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:  x = 11/2   or   x = 5.5

Steps:  -5(2x - 10) = 2(x - 8)

Expand: -10x + 50 = 2x - 16

Subtract 50 from both sides: -10x + 50 - 50 = 2x - 16 - 50

Simplify: -10x = 2x - 66

Subtract 2x from both sides: -10x - 2x = 2x - 66 - 2x

Simplify: -12x = -66

Divide both sides by 12:  -12x ÷ 12  =  -66 ÷ 12

Simplify: x = 11/2   or    5.5

Plz mark brainliest:)

Answer:

26.24 dollars per hour

Answer:

$26.24 each hour

hope it helps :)

Step-by-step explanation:

131.20/5=26.24

Answer:

-7/3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( 7 - -7)/(-3 -3)

    = ( 7+7)/( -6)

    = 14/-6

   = 7/-3

   = -7/3

Step-by-step explanation:

m = y2-y1 / x2-x1

= 7+7 / -3-3

= 14/-6

= -7/3

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

4\(y^{\frac{3}{2} }\)

Step-by-step explanation:

using the rule of exponents/ radicals

\(\sqrt[n]{a^{m} }\) = \(a^{\frac{m}{n} }\)

then

4 \(\sqrt{y^{3} }\)

= 4\(y^{\frac{3}{2} }\)

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer:

Instead of adding the exponents of 2 to get four you should just leave the exponent as two in the final answer.

The length of a football field should be measured in yards

Hi! I'm happy to help!

We know that a football field is separated into 100 (numbers marked on the field.) A football field is also 100 yards, so it would be reasonable to measure it in yards.

I hope this was helpful, keep learning! :D

Answer:

  the slope is 1, the coefficient of x.

Step-by-step explanation:

You want to know the mistake in declaring the slope of y=x is 0, because there is no coefficient.

In algebra, a coefficient of 1 is usually not written. We let 1 times something be represented by the something itself. Its existence is indication there is one of it. No multiplier is needed.

  y = x   ⇔   y = 1·x

Whether the 1 is there or not, there is still exactly one 'x'.

So, the coefficient of x is 1 in y=x, meaning the slope is 1, not zero.