A boat is heading towards a lighthouse, whose beacon-light is 140 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 10∘∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest tenth of a foot if necessary.

Since the graph gives us the relative frequency we just have to add those who are more or equal to 16; in this case we have to add 0.11 and 0.06, therefore the proportion in this case is 0.17

Ok, so the equation is (2/5)m=8

1st option: Divide by 2 on both sides, then multiply by 5 on both sides:

2nd option: Multiply both sides by 5/2

3rd option: First dristibute 2/5 to (m=8), the multiply by 5/2 in both sides

4th option: Divide both sides by 2/5:

5th option: First, multiply by 5. Then, divide by 2.

All the methods are correct

ANSWER

EXPLANATION

We want to solve the given equation for w:

To do this, we have to factorize the equation and simplify it.

Let us do that now:

That is the answer.

First, find the hourly rate by dividing the total wage of $560 by the amount of time worked, which is 40 hours:

To find the hourly rate for overtime, multiply the basic hourly rate by 1.5:

Therefore, the hourly rate for overtime is $21.

The volume of a right rectangular prism is given by

From the given information, we know that

So, the volume is given by

which gives

Now, since the content weigh 0.18 pound per cubic foot and worth $7.18 per pound, the value of the container is given by,

Therefore, by rounding to the nearest cent, the answer is:

SOLUTION

Step 1: Make a more comprehensive sketch of the question.

The measure of CFE is 81 degrees.

To answer this question, we need to transform each of the values into the corresponding other units:

• Inches ---> Feet

• Week ---> minutes

And we also have here a ratio:

• Inches/week ---> Feet/minute.

Then we can proceed as follows:

We know that the conversion between inches and feet is:

Then

If we have 9,400 inches, then:

We know that:

In one day we have 24 hours, then:

Then we have 1440 minutes in a day. A week has 7 days. Therefore, we will have:

Therefore, we have that there are 10,080 minutes in one week.

Now, to find the ratio of feet per minute, we need to divide:

In summary, we can say that the object moves:

into the

Consider that the intercept form of equation of a line whose x-intercept is (a,0) and y-intercept is (0,b), is given by,

The equation of the line is given as,

Convert this equation into intercept form,

Comparing with the standard equation,

Thus, the x-intercept and y-intercept of the equation, respectively, are,

SOLUTION:

Step 1:

In this question, we are asked to calculate Chandler's gross pay from the statement of bi-weekly earnings.

Step 2:

To get the Gross pay, we need to do the following:

Now, we need to calculate Total Deductions:

Now, we have that the Net Pay = $ 780. 63

Then,

CONCLUSION:

Chandler's Gross Pay = $ 974. 54

1) Problems like these, we can solve by writing an equation.

2)Since that tomato plant grew 150% after three weeks we can write the following

Note that in the parentheses we have the factor of growth. Since it's 150% we can add to 1 and write 1 +1.5=2.5

3) Thus, the answer is:

Answer:

-$0.05

Explanation:

The expected value can be calculated as the sum of each possible prize multiplied by its probability. You will buy a ticket for $1 and there is a probability of 1/1000 to win the $500, a probability of 1/1000 to win $300, and a probability of 1/1000 to win $150, then the expected alue is

Therefore, the expected value is -$0.05.

Here,point can be written as:

The formula for the distance between the points as follows;

Thus, the distance between the point is 12.53.

To solve this question, we will apply the knowledge of exponents and indices

The values have the same bases (7) but different powers and they are separated by a multiplication sign.

So we can use the law:

so that

on simplifying will give

=>

Recall that:

1) f(x) is an even function if:

2) f(x) is an odd function if:

Now, notice that:

Therefore f(x)=3^x is neither an even function nor an odd function.

Answer: Neither an even function nor an odd function.

23 - 4u < 11

23 is adding on the left, then it will subtract on the right

-4u < 11 - 23

-4u < -12

-4 is multiplying on the left, then it will divide on the right. Remember that dividing by a negative number changes the sign.

u > (-12)/(-4)

u > 3

The most important reason for random assignment on the subjects in the experiment, is because random assignment would be the best way in creating group of subjects to the different treatments.

Note that; the group of subjects are roughly equivalent at the beginning of the experiment.

Using random assignment will allow the allocation of different patients to various treatments at a random order. From this there will be objective results obtained altogether from the experiment under investigation.

Random assignment will eliminate any biasness that may occur when conducting the experiment. It prevents favoritism of any event from occurring. It will ensure that all the different patients have an equal chance of being selected for various treatment.

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Answer:

The parent function of the graph is given below as

The parent function has undergone transformation

Hence,

Using a graphing calculator, we will have the graph be

Hence,

The final answer is

The FIRST OPTION is the right answer

The equation of the function has its domain representation in interval notation as (oo, oo)

From the question, the equation of the function is given as

f ( x ) = 6356 x + 5095

Rewrite the equation of the function properly by removing the excess spaces

So, we have

f(x) = 6356x + 5095

The above equation is a linear equation

A linear equation is represented as

f(x) = mx + c

As a general rule;

The domain of a linear equation is all set of real numbers

This is the same for the range

i.e. the range of a linear equation is all set of real numbers

When the set of real numbers is represented as an interval notation, we have the following representation

(oo, oo)

Hence, the domain is (oo, oo)

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Possible question

let f ( x ) = 6356 x + 5095 . Use interval notation to represent the domain of the function.

Many answers are possible.

Answer;

Explanation;

Firstly, we need a diagrammatic representation to get what is described in the question.

We have this as follows;

Now, from what we have here, the total angle swept by the pendulum moving from left to right is 28 degrees

To get the area, we simply need to find the area of the sector formed by the by pendulum

Mathematically, we have the area of a sector calculated as follows;

theta is the angle made by the pendulum in one complete swing which is 28 degrees

pi is 22/7

R is the length of the pendulum which is 14 cm

Substituting these values in the formula above, we have it that;

Firstly, we want to calculate the growth rate of the population

While birth would increase the population, death and migration will decrease the population

So when we subtract the migration rate and the death rate from the birth rate, we can get the population growth rate;

Thus, we have;

The national population growth rate for a country X is 12/1000

Secondly, we are to use the rule of 70 to calculate the doubling time for the population

Mathematically;

The difference between the graph of a radical function and that of a rational function is:

A radical graph is drawn from a function that contains a root, it could be a square root, cube root, etc. Whenever you are graphing a radical function, we first need to consider the domain. Because of the square root sign, the domain and range are always restricted.

But a rational graph is drawn from the ratio of two polynomial functions where the function in the denominator is not equal to zero. A rational graph is characterized by asymptotes.

The major difference would be that a radical graph has a restricted domain due to the root, and usually without an asymptote, while a polynomial graph has a restricted domain and sometimes range which forms the asymptote (vertical, horizontal asymptote).

→ r represents the original cost of the repair.

→ 0.07r represents the tax.

→ (r – 20) represents the discount

Given,

The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair.

Explain what each part of the expression represents in the context of the problem.

Now, According to the question:

Given the following algebraic expression:

0.07r + (r – 20)

In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.

What each part of the expression represents in the context of the problem include the following:

→ r represents the original cost of the repair.

→ 0.07r represents the tax.

→ (r – 20) represents the discount

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Let

x ----> amount deposited at 4.5%

y ----> amount deposited at 5%

we have that

y=2x----> equation A

4.5%=0.045

5%=0.05

so

0.045x+0.05y=1,595 ----> equation B

solve the system

substitute equation A in equation B

0.045(x)+0.05(2x)=1,595

solve for x

0.045x+0.10x=1,595

0.145x=1,595

x=11,000

Find y

y=2(11,000)=22,000

In the elimination method, we need to eliminate one of the variables using addition or subtraction.

In this case, if we add both equations, we have that:

Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.

In summary, using the elimination method, we add both equations. The result for that was a false r

0.3821,  0.8745

========================================================

Work Shown:

pi/2 = 3.14/2 = 1.57 approximately

The solutions for t must be in the interval 0 ≤ t ≤ 1.57

[tex]3\cos(5t)+3 = 2\\\\3\cos(5t) = 2-3\\\\3\cos(5t) = -1\\\\\cos(5t) = -1/3\\\\5t = \cos^{-1}(-1/3)\\\\5t \approx 1.9106+2\pi n \ \text{ or } \ 5t \approx -1.9106+2\pi n\\\\t \approx \frac{1.9106+2\pi n}{5} \ \text{ or } \ t \approx \frac{-1.9106+2\pi n}{5}\\\\[/tex]

where n is an integer.

Let

[tex]P = \frac{1.9106+2\pi n}{5}\\\\Q = \frac{-1.9106+2\pi n}{5}\\\\[/tex]

Then let's generate a small table of values like so

[tex]\begin{array}{|c|c|c|} \cline{1-3}n & P & Q\\\cline{1-3}-1 & -0.8745 & -1.6388\\\cline{1-3}0 & **0.3821** & -0.3821\\\cline{1-3}1 & 1.6388 & **0.8745**\\\cline{1-3}2 & 2.8954 & 2.1312\\\cline{1-3}\end{array}[/tex]

The terms with surrounding double stars represent items in the interval 0 ≤ t ≤ 1.57

Therefore, we end up with the solutions 0.3821 and 0.8745 both of which are approximate.

You can use a graphing tool like Desmos or GeoGebra to verify the solutions. Be sure to restrict the domain to 0 ≤ t ≤ 1.57

Answer:

[tex]\textsf{c)} \quad 0.3821, \; 0.8745[/tex]

Step-by-step explanation:

Given equation:

[tex]3 \cos (5t)+3=2, \quad \quad 0\leq t\leq \dfrac{\pi}{2}[/tex]

Rearrange the equation to isolate cos(5t):

[tex]\begin{aligned}\implies 3 \cos(5t)+3&=2\\3 \cos(5t)&=-1\\\cos(5t)&=-\dfrac{1}{3}\end{aligned}[/tex]

Take the inverse cosine of both sides:

[tex]\implies 5t=\cos^{-1}\left(-\dfrac{1}{3}\right)[/tex]

[tex]\implies 5t=1.91063..., -1.91063...[/tex]

As the cosine graph repeats every 2π radians, add 2πn to the answers:

[tex]\implies 5t=1.91063...+2\pi n, -1.91063...+2 \pi n[/tex]

Divide both sides by 5:

[tex]\implies t=0.38212...+\dfrac{2}{5}\pi n,\;\; -0.38212...+\dfrac{2}{5} \pi n[/tex]

The given interval is:

[tex]0\leq t\leq \dfrac{\pi}{2}\implies0\leq t\leq 1.57079...[/tex]

Therefore, the solutions to the equation in the given interval are:

[tex]\implies t=0.3821, \; 0.8745[/tex]

==================================================

Explanation:

Recall that

i = sqrt(-1)

Squaring both sides gets us

i^2 = -1

Now let's multiply both sides by i

i*i^2 = i*(-1)

i^3 = -i

Repeat the last step

i^3 = -i

i*i^3 = i*(-i)

i^4 = -i^2

i^4 = -(-1)

i^4 = 1

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

Here's a summary so far

The pattern repeats every 4 items. This means we'll divide the exponent by 4 and look at the remainder.

20/4 = 5 remainder 0

Therefore i^20 = i^0 = 1

Or we can think of it like this

i^20 = (i^4)^5 = 1^5 = 1

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

This means we can then say

i^3 + i^20 = -i + 1 = 1 - i

Answer:

Explanation:

Given the equation:

To solve an equation using the square root property, begin by isolating the term that contains the square.

After isolating the variable that contains the square, take the square root of both sides and solve for the variable.

Therefore, the solutions to the equation are:

The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:

[tex]y = \frac{1}{4} x-5[/tex].

These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.

Given equation of line is:

y=-4x + 5

Let [tex]m_{1}[/tex] be the slope of given line

Then,

[tex]m_{1}[/tex] = -4

Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line

As we know that product of slopes of two perpendicular lines is -1.

[tex]m_{1}*m_{2} = -1\\- 4*m_{2}=-1\\ m_{2} = \frac{1}{4}[/tex]

The slope intercept form of line is given by

[tex]y = m_{2}x+c[/tex]

[tex]y = \frac{1}{4} x+c[/tex]

to find the value of c, putting (4,-1) in equation

[tex]-3= \frac{1}{4} *8+c\\-3-2 = c\\c = -5[/tex]

Putting the value of c in the equation

  [tex]y=\frac{1}{4} x-5[/tex]

Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is    [tex]y=\frac{1}{4} x-5[/tex].

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