An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 6° and θ = 10.5° (see figure). How far apart are the ships? (Round your answer to one decimal place.) ft

The list of all sets which are subsets of the given set; {Lennon, McCartney} as required is; { }, {Lennon}, {McCartney}, {Lennon, McCartney}.

It follows from the task content that the list of all subsets of the given set is to be determined.

It is noteworthy to know that the empty set, {} is a subset of all sets.

Also, if all the elements of a set A are present in another set B; it can be inferred that the set A is a subset of set B.

On this note, the list of all sets which are subsets of the given set; {Lennon, McCartney} is; { }, { Lennon }, { McCartney }, { Lennon, McCartney }.

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A graph of the absolute function y = |x + 2| - 4 with five points that fit on the axes is shown in the image attached below.

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).

Next, we would use an online graphing calculator to plot the given absolute value function y = |x + 2| - 4 as shown in the graph attached below.

By observing critically the graph (see attachment), the five ordered pairs (points) that fit on its axes include the following:

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Answer:

6

Step-by-step explanation:

85 +12.5*x visits =155

12.5x≥70

x must be greater than 5.6 so she need to go 6 times & then she'll get her free ticket

The interest paid at the term end will be $5400.

What is interest and its types(Simple and compound interest)?

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

​The formula for these are

Simple Interest= P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

Compound Interest=P×(1+r)^t−P

where:

P=Principal amount

r=Annual interest rate

t=Number of years interest is applied

Here,

Interest rate will be risk percentage + LIBOR

i.e.4.8%

Hence,  the interest can be found by using formula for simple interest

Therefore,

SI=P*r*t

=$450000*0.048*0.25               (Time is 3 month or  0.25 years.)

SI (Interest paid)=$5400

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The total interest paid for the period of three months will be $5225 on the loan amount of $450000.

What is interest?

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $450000

R=2.2%+2.8%=5%

T=1/4 years or three months

So from the simple interest formula

SI= PNR/100

SI=15000×5×1/`100×4

SI=$5625

Hence the total interest paid for the period of three months will be $5225 on the loan amount of $450000.

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Answer:

2y+x=7

Step-by-step explanation:

The equation of a line is in the form:

[tex]y = mx + c[/tex]

where m is the gradient and c is the y-intercept.

In the equation y=2x+3 the gradient is 2, so to find the perpendicular gradient, it is the negative reciprocal, or in other words, flip the number upside down and make it negative:

[tex]2 = \frac{2}{1} [/tex]

[tex] \frac{2}{1} \: flipped \: upside \: down = \frac{1}{2} [/tex]

[tex] make \: \frac{1}{2} \: negative = - \frac{1}{2} [/tex]

So the gradient for the point (1, 3) is -1/2

Using y=mx+c to find c (the y-intercept) where y=1, m=-1/2, x=1, substitute these values in:

[tex]y = mx + c[/tex]

[tex]3 = - \frac{1}{2} (1) + c[/tex]

[tex]3 = - \frac{1}{2} + c[/tex]

[tex]3 + \frac{1}{2} = c[/tex]

[tex]c = \frac{7}{2} [/tex]

So the equation is:

[tex]y = - \frac{1}{2} x + \frac{7}{2} [/tex]

We need to write this in the form ax+by=c, so multiply everything by 2 to get rid of the fractions on the right:

[tex]2y = - x + 7[/tex]

Bring x to the left side by adding it:

[tex]2y + x = 7[/tex]

This is now in the form ax+by=c

Answer:

A=4.2 P=9.2

Step-by-step explanation:

Did this also and used mathaway

If In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46° then the length of g is 800 inches.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The sum of interior angles of a triangle are 180 degrees.

In ΔEFG, e = 690 inches, ∠F=94° and ∠G=46

We need to find the ∠E then the length of g.

∠E+∠F+∠G=180

∠E+94+46=180

∠E+140=180

∠E=40 degrees

By using sinE rule we have to find the length of g.

SinE/E=sinG/G

sin40/690=sin46/x

0.642/690=0.72/x

0.00093=0.72/x

x=0.72/0.0009

x=800 inches

Hence, the length of g is 800 inches.

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Answer:

Question 4:

Question 5:

Question 6:

Step-by-step explanation:

Given vertices of the pre-image:

If the pre-image is reflected in the line x = -1, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 180° about the origin, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 270° about the origin, the transformation rule is:

If the direction of a rotation is not specified, then it is counterclockwise.

Therefore the vertices of the image are:

Answer:

A= 110 degrees AND B= 140 degrees.

Y= 112 degrees and X= 157 degrees.

Step-by-step explanation:

Triangle XYZ is an isocoles triangle, because it has two congruent sides. 70 degrees is a measurement of an angle opposite of one of those congruent sides, so angle YXZ is also 70 degrees. By the triangle angle sum theorem, we can say that the measurement of angle YZX is 40 degrees. So, for the first triangle, by the linear pairs theorem, we can find the two missing angles.

A= 110 degrees AND B=140 degrees.

For the triangle on the right, we can use the triangle angle sum theorem to say that angle BDC is 68 degrees. Then, we can say that by the by the linear pairs theorem that angle ADE is 112 degrees.  From there, we need to look at the 23 degree measurement on the lower right triangle. We can see that the angle steadily rises on that line and then we can take 180-23 by the linear pairs theorem to conclude than angle BEA is 157 degrees. This can be confirmed by looking at the two innermost angles in the top right triangle. If you take 180-23-112, you will get 45. If you add 45 to 112, you will get 157.

Y= 112 degrees and X= 157 degrees.

Answer:

Step-by-step explanation:

If you used good technique, you would expect the range of measurements to be small. Good technique would include using a measuring instrument that is calibrated correctly, measuring in the same position and at the same time of day, and being consistent in how you position your body during the measurement. All of these factors would help to reduce the amount of measurement error and therefore lead to a smaller range of measurements.

On solving the provided question, we can say that the value of the quadratic equation would be x = 0.18

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

The given equation is 2x² + 5x - 1 = 0

Hence, the larger root of the given quadratic equation would be x = 0.18.

[tex]x = \frac{-5 + \sqrt{5^2 - 4(2)(-1)} }{2(2)} \\x = 0.18\\or \\x = -2.68\\[/tex]

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Answer:

1. Nevoia de a te certa sau de a-i critica pe cei din familie prin limbaj cu conotatii negative sau prin tonul vocii.

2. Nerespectarea deciziilor familiei sau nerespectarea responsabilitatilor asumate.

3. Abuzul verbal sau emotional, inclusiv insultele sau minciunile.

4. Negarea dreptului la intimitate sau la spatiu personal.

5. Ignorarea afectiunii si a momentelor importante din familie.

Answer: 96 Euros each month

Step-by-step explanation: 2400 * 0.2 = 480 -> 2400-480 = 1920(this is the amount of money needed to pay each month) 1920 / 20 = 96

1.) The 50% of R100 = R50

2.) The 0.5 of R100 = R50

3.) The ½ of R100 = R50.

Percentage is defined as the part of a whole which is represented per 100 and the symbol which is used is %.

Therefore, is can be concluded since the same value was gotten that 50% = 0.5 = ½.

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The latera surface area of the triangular prism is  425 inches².

The isosceles triangular prism is unfolded into the net shown below. Therefore, the lateral surface area of the triangular prism can be found as follows:

The lateral surface area of the triangular prism is the product of the perimeter of the triangle and the height of the prism.

Hence,

lateral surface area of the triangular prism = ph

where,

Therefore,

lateral surface area of the triangular prism = (9 + 9 + 7)17

lateral surface area of the triangular prism = 25 × 17

lateral surface area of the triangular prism = 425 inches²

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Answer:

39000meter

hope it will help you

The domain of the function is  (-∞, 1), (1, ∞).

the correct option is (C)

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Given:

As, we know the domain are the input values in the function.

So, From the graph the domain starts from -∞ to reach 1 then there is change in slope.

Next the domain starts from  to ∞.

Now, range is the output value as (-4, 1).

Hence, the domain is (-∞, 1), (1, ∞).

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A relative maximum is a highest point in that little area.  Think of it as a top to a mountain in a mountain range.  It's a peak, but it might not be the tallest peak.

A relative minimum is the lowest point in that little area.  Think of it as a the bottom of a valley in some area.  It's possibly one of many valleys, so might not be the deepest valley.

When we talk about where these things happen, we describe them based on their x-values.  They happen at the x-value of that peak or valley.

There's a little peak on the left side and the x-value of that peak is x = -1.2.

There's a little valley on the right side and the x-value of that valley is x = 1.2.

The answer is A.

Step-by-step explanation:

different between each value is 4

well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}[/tex]

Answer: r <= -24.32
CMIIW :))

Step-by-step explanation:

Answer:

1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step-by-step explanation:

All of these are factors of 36.

They can all be divisors with no remainder

Answer: The area of the floor of the store room is 1080 m^2

Step-by-step explanation:

We can begin by using the information provided about the ratios of the dimensions of the store room to set up a system of equations.

Let's call the height of the store room h, the length l, and the breadth b.

From the first ratio given, we know that:

h/l = 5/4

From the second ratio given, we know that:

h/b = 2/3

We can also use the information about the total area of the four walls to set up another equation.

The total area of the four walls is the sum of the area of the top and bottom walls (length x height) and the area of the two side walls (breadth x height).

So we have:

2lh + 2bh = 2760

We can now use the first two equations to solve for one of the variables in terms of the other two.

We can cross-multiply and simplify the first equation:

l = (4/5)h

We can cross-multiply and simplify the second equation:

b = (3/2)h

We can now substitute these expressions for l and b into the equation for the total area of the four walls:

2(4/5)h^2 + 2(3/2)h^2 = 2760

Solving for h, we get:

h = 30

Now that we know the value of h, we can use the equations l = (4/5)h and b = (3/2)h to find the values of l and b.

l = (4/5)h = (4/5)(30) = 24

b = (3/2)h = (3/2)(30) = 45

Now we have all the information we need to find the area of the floor, which is the product of the length and breadth of the store room

Area of floor = lb = 2445 = 1080 m^2

Explanation: By using the information about the ratios of the dimensions of the store room and the total area of the four walls, we set up a system of equations and used algebra to solve for the height, length and breadth of the store room. With this information, we were able to find the area of the floor of the store room.

Answer: 3

Hope this helps :)

Step-by-step explanation:

1+2+3+4+5=15

15/5=3

The term that represents the cost of the shoes after the discount is (1 - 0. 025)s. Option D

Algebraic expressions are described as mathematical expressions that consist of factors, constants, variables, terms and coefficients.

They are also made up of arithmetic operations, which includes;

From the information given, we have that there was a 25% discount on all the shoes Declan bought

Given the expression;

c + ( 1 - 0.25)s + 0. 08[c + (1 -0.25)s ]

expand the bracket

c + s - 0. 25s + 0. 08( c - s - 0. 25s)

expand the parentheses

c + s - 0. 25s + 0. 08c - 0. 08s - 0.02

But for the cost of the shoes after the 25% discount, we have;

(1 - 0. 025)s

Hence, the expression is (1 - 0. 025)s

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Answer:

Step-by-step explanation:

The solutions to this equation are x = 1.273 and x = -0.273.

When x = 1.273, 3 cos (x) + 4 = 5.

When x = -0.273, 3 cos (x) + 4 = 5.

Rounding to 3 decimal places, the solutions to the equation on the indicated interval are x = 1.273 and x = -0.273.

Answer:

a) n(A)7

b) 140

Step-by-step explanation:

a) numbers in the set

b)since n(A)=7

20A=20×7

=140

Answer:

  (-20x -25)/(x^2-x-30)

Step-by-step explanation:

You want to simplify the rational expression (3x²)/(x²-x-30) -(3x+5)/(x-6).

Usually these problems are constructed so that the higher-degree polynomial denominator has the lower degree denominator as a factor. That is the case here.

  [tex]\dfrac{3x^2}{x^2-x-30}-\dfrac{3x+5}{x-6}=\dfrac{3x^2}{(x+5)(x-6)}-\dfrac{(x+5)(3x+5)}{(x+5)(x-6)}\\\\=\dfrac{3x^2-(3x^2+20x+25)}{x^2-x-30}[/tex]

  [tex]=\boxed{\dfrac{-20x-25}{x^2-x-30}}[/tex]

The geom_ jitter () method creates a scatter plot and then it adds a small amount of random noise to every point in the plot to make the points easier to find.

Therefore, the geom_jitter is shortcut that creates a scatterplot and add random variation in each point.

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