I need help with this word problem please

A person in a lighthouse, that is 315ft high, spots a boat in trouble. The angle of depression to the boat is 21°49ʹ. How far from shore is the boat?

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Answer:

9√2

Step-by-step explanation:

a^2+b^2=c^2

a^2+b^2=18^2

a^2+b^2=324

324 ÷ 2 = 162

162 + 162 = 324 (on a 45 45 90 right triangle)

81 and 2 are factors of 162

square root of 162

√162 = √81 * 2  = 9√2

None of the given ordered pairs (9,5), (5,4), (6,6) and (3,4) is a solution to the inequality y > x + 3.

Given the inequality in the question:

y > x + 3

Also, given the ordered pairs: (9,5), (5,4), (6,6), (3,4).

To determine which of the given ordered pairs is a solution to the inequality y > x + 3,

we can substitute the values of x and y from each pair into the inequality and check if it holds true.

Checking for: (9,5)

y > x + 3

Is 5 > 9 + 3?

Is 5 > 12?

No, this inequality is not satisfied, so (9, 5) is not a solution.

(5, 4):

y > x + 3

Is 4 > 5 + 3?

Is 4 > 8?

No, this inequality is not satisfied, so (5, 4) is not a solution.

(6, 6):

y > x + 3

Is 6 > 6 + 3?

Is 6 > 9?

No, this inequality is not satisfied, so (6, 6) is not a solution.

(3, 4):

Is 4 > 3 + 3?

Is 4 > 6

No, this inequality is not satisfied, so (3, 4) is not a solution.

Therefore, none of the given pairs is a solution.

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Answer:

no neither of them are correct they both got the answer wrong because they didn't get the correct number because they didn't do the right steps to get the right answer.

Step-by-step explanation:

well it =141328480. Conner's work equals out to be 1013. Jana's works out to be 338800. Making them both wrong but Jana being the closet to the right answer because since there is no symbol telling you what to do and it is in () then you would be multiplying the two numbers in the ().

Answer: Graph it!!!!!!!!!!!!!!!!!!!!!!

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Answer:

See below

Step-by-step explanation:

4 sin^2 -1 =0

sin^2 = 1/4          Take sqrt of both sides

sin = ± 1/2       < ===== this is likely where he went wrong (forgot + - )

 answer:  pi/6    5pi/6    7 pi/6     11pi/6

To find the z-score for a sales associate who earns $37,500, we can use the formula:

z = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, $37,500),

μ is the mean of the distribution (in this case, $32,500), and

σ is the standard deviation of the distribution (in this case, $2,500).

Substituting the given values into the formula, we have:

z = (37,500 - 32,500) / 2,500

z = 5,000 / 2,500

z = 2

Therefore, the z-score for a sales associate who earns $37,500 is 2.

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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.

The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.

We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:

Z = (Value - Mean) / Standard Deviation

So, the z-score for an associate earning $37,500 would be:

Z = ($37,500 - $32,500) / $2,500

This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.

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Answer:

angle 6 is 30 degrees

Step-by-step explanation:

its because 180/6 = 30

and 30 x 5 = 150 and 150 + 30 =180

hope this helps

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Answer:

--------------------

We see x - 2 is the common factor in the given expression.

Simplify as:

Answer:

10x - 20

Step-by-step explanation:

distribute the 3 and the 7 into the parentheses, getting you to (3x - 6) + (7x - 14), from there you should be able to just combine the like terms getting you to 10x - 20.

In order to find g(0), we just need to find the value of the function for x = 0.

Looking at the graph, for x = 0 we have y = 7.

Therefore g(0) = 7.

To find the value of x for g(x) = -1, let's look for the value of x where y = -1.

Looking at the graph, for y = -1, we have x = -2.

Therefore g(x) = -1 for x = -2.

Answer:

120 cookies

Step-by-step explanation:

3 / (3/4) = 4

30 * 4 = 120

Answer:

120

Step-by-step explanation:

3/4 of an hour is the same as 45 minutes. If she is doing this in an even pace, we can figure out how many cookies she's made in 15 minutes. (This will make the problem easier for us to solve.)

45÷3=15

30÷3=10

We now that in 15 minutes she can make 10 cookies. There are 180 minutes in three hours so we can divide 180 by 15 to know how many rounds of 15 there is.

180÷15 =12

Know we know that there are 12 rounds of 15 in three hours. We also know that in 15 minutes she can make ten cookies so all we have to do now is to multiply 12×10 to get 120. She can make 120 cookies in three hours.

Answer:

4/19

Step-by-step explanation:

The distance Jon travels to work is 472.5 miles.

Let d be the distance Jon travels to work.

The time it takes to drive is 20 minutes and the time it takes to bike is 45 minutes.

The difference in speed between driving and biking is 14.5 mph.

We can set up the following equation:

20min * (14.5mph + x) = 45min * x

Solving for x gives us the average speed of Jon on the bike, which is 10.5 mph.

Now we can use the distance formula to solve for d:

d = rate * time

d = 10.5mph * 45min

d = 472.5 miles

Therefore, the distance Jon travels to work is 472.5 miles.

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Answer:

77 degrees

Step-by-step explanation:

supplementary angles add up to 180 degrees

subtract 103 from 180 to get 77 degrees

The factored function is given as follows:

\(x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)\)

The function for this problem is defined as follows:

\(y = x^4 + 2x^3 - 20x^2 + 64x - 32\)

The zeros are given as follows:

Hence the function is factored as follows:

\(x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x - 2 + 2i)(x - 2 - 2i)\)

\(x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x^2 - 4x + 8)\)

\(x^4 + 2x^3 - 20x^2 + 64x - 32 = ax^4 + (-4 + b)x^3 + \cdots + 8c\)

Hence the value of a is given as follows:

a = 1.

The value of b is given as follows:

-4 + b = 2

b = 6.

The value of c is given as follows:

8c = -32

c = -4.

Hence the factored expression is of:

\(x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)\)

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The dependent variable in this hypothesis is test performance.

What is a dependent variable?

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, one‘s values are examined under the assumption as well as demand that they are dependent on the value of another variable due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not thought to be depending on other variables. Time, space, specific gravity, mass, fluid flow rate and previous values of certain observed value of interest (such as the size of the human population) are examples of common independent variables that can be used to forecast future value systems (the dependent variable).

The outcome of this hypothesis is the dependent variable.

Hence, the dependent variable in this hypothesis is test performance.

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The possible volume of cylinder is  V= \(\frac{4\sqrt{3}\pi r^3 }{9}\)  .

What is Volume ?

A three-dimensional space's occupied volume is measured. It is frequently expressed numerically in terms of SI-derived units or different imperial units. Volume definition and length definition are connected.

There are several steps to this optimization problem.

1.) Find the equation for the volume of a cylinder inscribed in a sphere.

2.) Find the derivative of the volume equation.

3.) Set the derivative equal to zero and solve to identify the critical points.

4.) Plug the critical points into the volume equation to find the maximum volume.

Given the height, h , we can find the radius of the cylinder in terms of r

using the Pythagorean Theorem.

Note that h refers to half of the total height of the cylinder. I chose to use h instead of  \(\frac{h}{2}\) to simplify things later on.

To find the volume of our cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;

V= π \((radius of cylinder)^2 * (height of cylinder)\)

=> V = π (\((\sqrt{r^2-h^2} )^2\) (2h)

=> V = 2πh \((r^2-h^2)\)

This is our volume function. Next we take the derivative of the volume function and set it equal to zero. If we move the h inside the parenthesis, we only need to use the power rule to get the derivative.

=>V = 2π \((r^2h-h^3)\)

=> V= \(\frac{4\sqrt{3}\pi r^3 }{9}\)

This is the optimized volume for the cylinder. Its a good check to notice that V is in terms of \(r^3\) since volume should have cubic units. In other words, if our radius was given in term of meters, our volume units would be \(m^3\) .

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Answer:

7x+y, when x+4 and y+5

7(4) + 5=

28+5=

33

Step-by-step explanation:

Hope this helps. :)

Answer:

no, h=anything greater than 12

Step-by-step explanation

Answer:

No. It is false.

Step-by-step explanation:

h - 2 > 10; h = 12

Substitute 12 in place of h.

12 - 2 >? 10

Simplify.

10 >? 10

10 is NOT > 10

10 is not greater than 10. 10 is equal to 10. If the symbol had the "or equal to" underline under it, then it would be true. See image.

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

In explanation

Step-by-step explanation:

The conversion equation for the weight from Earth to Jupiter can be expressed as the following:

\(J=\frac{E}{9.81} (24.79)\\\)

We have the weight already as in Jupiter, so we'll work backwards:

2450=E/9.81(24.79)

E=970 (969.5 estimated)

Hope this helped! Have a good day.

Answer:

Step-by-step explanation:

The frame is rectangular in nature, to determine a reasonable value for how much wall space the portrait will cover, we will take the area of the frame.

Given

Length of the frame = 45in

Width of the frame = 37in

Required

Area of the frame

Area of the rectangular frame = Length * Breadth

Area of the rectangular frame = 45in * 37in

Given 1feet = 12in

45in = 45/12 ft=  3.75ft

37 in = 37/12 ft = 3.083 ft

Area of the frame = 3.75ft * 3.083 ft

Area of the frame = 11.56ft²

Area of the frame ≈ 12ft²

For the two given statements are:

"For every dollar you spend, you can get pounds of grapes."

If one pound costs $2, then for each dollar you will get half a pound.

"For each pound of grapes, you would need"

For each pound of grapes you will need 2 dollars.

Here we know that the graph shows the relationship between the pounds of grapes (g) and the cost (c). Such that the cost is on the horizontal axis, and the weight on the vertical axis.

We have the points:

Then this is a proportional relationship, and we can see that each pound of grapes costs $2

Then the statements are:

1) "For every dollar you spend, you can get pounds of grapes."

If one pound costs $2, then for each dollar you will get half a pound.

2) "For each pound of grapes, you would need"

For each pound of grapes you will need 2 dollars.

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The standard deviation of the data set is 3.17 (rounded to the nearest tenth).

To calculate the standard deviation of a set of data, you first need to calculate the mean (average) of the data set.

Mean = (17 + 18 + 22 + 16 + 18 + 14 + 13 + 23 + 20) / 9 = 18

Next, you need to calculate the variance of the data set.

Variance = [(17-18)^2 + (18-18)^2 + (22-18)^2 + (16-18)^2 + (18-18)^2 + (14-18)^2 + (13-18)^2 + (23-18)^2 + (20-18)^2] / (9-1) = 18.7

Standard deviation = √(18.7) = 3.17

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Answer:

Step-by-step explanation:

divide 4 and 2 then add 2 and 1

Answer:

y = - 4x + 17

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (4, 1) and (x₂, y₂ ) = (2, 9)

m = \(\frac{9-1}{2-4}\) = \(\frac{8}{-2}\) = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 1) , then

1 = - 16 + c ⇒ c = 1 + 16 = 17

y = - 4x + 17 ← equation of line

Answer:

d=√((x_2-x_1)²+(y_2-y_1)²)

Step-by-step explanation:

which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points