simplify: -2y + 3y2 – 3y + y

The correct answer from each drop-down menu is:

If cost 8 = 8 and tan20 = 17, then cos28 = -8/17.

To solve this problem, we can use the double angle formula for cosine:

cos2θ = 2cos²θ - 1

We know that cos20 = 17, so we can substitute this value into the formula:

cos2(20°) = 2(cos20°)² - 1

cos2(20°) = 2(17²)² - 1

cos2(20°) = -8/17

Therefore, the correct answer is cos28 = -8/17.

Answer:

Ostrich can run in 5 second = 105 meter .

Step-by-step explanation:

Given  : The double number line shows that in 3 seconds an ostrich can run 63 meters .

To find : Based on the ratio shown in the double number line how far can the ostrich run in 5 seconds.

Solution : We have given

ostrich can run in 3 second = 63 meter .

Let ostrich can run in 5 second = x meter .

By the Ratio : 63 : 3 :: x : 5

[tex]\frac{63}{3} =\frac{x}{5}[/tex]

On cross multiplication

63 * 5 = 3 * x

315 = 3 x

On dividing both sides by 3

x = 105 meter .

Therefore, ostrich can run in 5 second = 105 meter .

Answer:

Jeff mows 9 yards of lawn in 30 minutes

Step-by-step explanation:

The equation that models the amount of time (t) in minutes it takes Jeff to mow an average sized yard is [tex]t=2n+12[/tex], where n is the number of yards he mows.

To find the number of yards Jeff mows in 30 minutes, we set the equation to 30 and solve for n.

[tex]\implies 2n+12=30[/tex]

Add -12 to both sides:

[tex]\implies 2n=30-12[/tex]

[tex]\implies 2n=18[/tex]

Divide both sides by 2

[tex]\implies \frac{2n}{2}=\frac{18}{2}[/tex]

[tex]\implies n=9[/tex]

Hence Jeff mows 9 yards of lawn in 30 minutes.

Final answer:

Jeff mows 9 lawns if it takes him 30 minutes, based on the equation t = 2n + 12

Explanation:

The question asks us to find out how many lawns Jeff mows if it takes him 30 minutes. The relationship between the amount of time (t) in minutes and the number of yards he mows (n) is given by the equation t = 2n + 12. Since we are given that t = 30 minutes, we can substitute the value of t into the equation to solve for n, the number of lawns.

30 = 2n + 12

By subtracting 12 from both sides of the equation we get:

18 = 2n

Next, we divide both sides of the equation by 2 to solve for n:

n = 9

Therefore, Jeff mows 9 lawns if it takes him 30 minutes.

Answer:

Step-by-step explanation:

Angles 1 and 3 are vertical angles, so are equal:

  m∠1 = m∠3 = 43°27'

Angles 2 and 3 are a linear pair, so are supplementary:

  m∠2 = 180° - m∠3 = 180° - 43°27' = 136°33'

Angles 2 and 4 are also vertical angles, so are equal:

  m∠4 = m∠2 = 136°33'

_____

There are 60 minutes in a degree, so 180° is the same as 179°60'. Subtraction can proceed in the usual way after this rewrite:

  180° - 43°27' = 179°60' -43°27'

  = (179 -43)° +(60 -27)' = 136°33'

There were 26 fans at the game who were lucky enough to receive all three free items.

The Madd Batters minor league baseball team offered different incentives to its fans for the opening home game.

To determine how many fans were lucky enough to receive all three free items, we need to find the total number of fans that satisfy each condition.

The least common multiple of 75, 30, and 50 is 150.

So, we divide 4000 by 150 to find the number of fans that satisfy the conditions for all three items.

Therefore, 26 fans at the game were lucky enough to receive all three free items.

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Answer:

B: between 1 and 2

Step-by-step explanation:

Since you share 5 kg amongst 4 you need to divide it by 4.

5 / 4 = 1.25 kg

This is between 1 and 2 kg

Answer: B. Between 1 and 2 kilograms.

Step-by-step explanation: Divide the amount of coffee by the number of people.

5/4=1.25.

Each person will get 1.25 kilograms of coffee, which is between 1 and 2 kilograms.

For this case we have to graph, we can see in the figure that the graph of the Neperian logarithm grows faster than the graph of the logarithm.

The graph of ln (x) is the second attached

Answer:

Option A

The log (x) graph will grow slower than the ln (x) graph.

See attached image

Find the common ratio between each number given:

8/4 = 2

16/8 = 2

32/16 = 2

The common ratio is constant at 2, which means the next number would be 32 x 2.

A geometric series equation is written as an = a1r^n-1

Where a1 is the first term, r is the ratio and n is the term you want to find.

r was determined to be 2. The first term is given as 4 ( the first number in the series).

This means the equation becomes an = 4(2)^n-1

The answer would be B.

Answer:

The answer is B

Step-by-step explanation:

Answer:

so, I believe D and E, are Binomials.

Step-by-step explanation:

Bi- is 2

Mono- is 1

Hope my answer has helped you and if not i'm sorry.

Answer:

The probability that the sample will contain exactly three​ successes is 0.2668.

Step-by-step explanation:

Given information:

Sample size = 10

Probability of a success, p=0.30

Probability of a failure q=1-p = 1-0.30 = 0.70

The binomial formula to determine the probability is

[tex]P(X=r)=^nC_rp^rq^{n-r}[/tex]

where, n is the sample size, r is required number of success, p is probability of success and q is probability of failure.

We need to find the probability that the sample will contain exactly three​ successes.

[tex]P(X=3)=^{10}C_3(0.30)^3(0.70)^{10-3}[/tex]

[tex]P(X=3)=^{10}C_3(0.30)^3(0.70)^{7}[/tex]

[tex]P(X=3)=(120)(0.0022235661)[/tex]

[tex]P(X=3)=0.266827932[/tex]

[tex]P(X=3)\approx 0.2668[/tex]

Therefore the probability that the sample will contain exactly three​ successes is 0.2668.

Using the binomial distribution, it is found that there is a 0.2668 = 26.68% probability that the sample will contain exactly three​ successes.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that the sample will contain exactly three​ successes is P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = x) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.2668[/tex]

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21

Step-by-step explanation:

Answer:

company A because its less money

Step-by-step explanation:

Answer:

Conjugate radicals.

Step-by-step explanation:

The two roots a+sqrb and a-sqr b are called conjugate radicals.

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

[tex](1.05)^x=1.885[/tex]

In order to solve for x, we have to get it out from its position of an exponent.  Do that by taking the natural log of both sides:

[tex]ln(1.05)^x=ln(1.885)[/tex]

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

[tex]x=\frac{ln(1.885)}{ln(1.05)}[/tex]

Do this on your calculator to find that

x = 12.99294297

For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

[tex]ln(x*x^2)=5[/tex]

Simplifying gives you

[tex]ln(x^3)=5[/tex]

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

[tex]ln(x)=\frac{5}{3}[/tex]

Take the inverse ln by raising each side to e:

[tex]e^{ln(x)}=e^{\frac{5}{3}}[/tex]

The "e" and the ln on the left undo each other, leaving you with just x; and raising e to the power or 5/3 gives you that

x = 5.29449005

For c. begin by dividing both sides by 20 to get:

[tex]\frac{1}{2}=e^{.1x}[/tex]

"Undo" that e by taking the ln of both sides:

[tex]ln(.5)=ln(e^{.1x})[/tex]

When the ln and the e undo each other on the right you're left with just .1x; on the left we have, from our calculators:

-.6931471806 = .1x

x = -6.931471806

Question d. is a bit more complicated than the others.  Begin by turning the base of 4 into a base of 2 so they are "like" in a sense:

[tex](2^2)^x-6(2)^x=-8[/tex]

Now we will bring over the -8 by adding:

[tex](2^2)^x-6(2)^x+8=0[/tex]

We can turn this into a quadratic of sorts and factor it, but we have to use a u substitution.  Let's let [tex]u=2^x[/tex]

When we do that, we can rewrite the polynomial as

[tex]u^2-6u+8=0[/tex]

This factors very nicely into u = 4 and u = 2

But don't forget the substitution that we made earlier to make this easy to factor.  Now we have to put it back in:

[tex]2^x=4,2^x=2[/tex]

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

[tex]2^2=2^x[/tex]

Now that the bases are the same, we can say that

x = 2

For the second solution, we will raise the 2 on the right to a power of 1 to get:

[tex]2^x=2^1[/tex]

Now that the bases are the same, we can say that

x = 1

Answer:

B) There is a gap in Plot A, but not in Plot B.

Step-by-step explanation:

Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of hours ten boys watched television over the same period of time. There is a gap in Plot A, but not in Plot B compares the shape of the dot plots.

The correct answer is B) There is a gap in Plot A, but not in Plot B

Explanation:

A dot plot is a type of graphic used in statistics to show information collected about a group of subjects or elements. In this, each dot or circle represents a subject related to a specific scale for example, in the case presented, the scale is the number of hours subjects watched television.

According to this, the statement that is true about the dot plots presented is that there is a gap in plot A because most subjects reported watching television for 3 to 7 hours; however, one of the subjects watched television 10 hours. This implies, a gap or space in the graphic because there is an interval in the scale with no subjects as most are grouped in a cluster except by one. This does not occur in plot B because all subjects form one cluster or group.

Answer:

The length of rectangular plot of land is 160 ft.

Step-by-step explanation:

L = 2 W (the length is twice the width)

P = 480 ft. (perimeter of rectangular plot of land)

L = ?

2. 2W + 2W= 480 ft  >>> (2 times twice width=L) + 2W=480 ft.

4W + 2W= 480 ft >>>> 6W= 480 ft.

W= 80 ft.

L = 2. 80 = 160 ft. (Length is twice the width)

P= 2L + 2W (formula for the perimeter)

2. 160 + 2. 80 = 480 ft.

Answer:

30°

Step-by-step explanation:

The measure of the arc is the same as the measure of the central angle that intercepts it, hence

m AC = ∠BAC = 30°

Answer:  The measure of arc BC is 30°

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Central\ angle = Intercepted\ arc[/tex]

Therefore, in this case, knowing that the angle BAC (which is the central angle) in the circle provided measures 30 degrees, you can conclude that the measure of arc BC (which is the intercepted arc) is 30 degrees.

Then you get that the answer is:

[tex]BAC=BC[/tex]

[tex]BC=30\°[/tex]

Answer:

Step-by-step explanation:

Such questions generally arise in the context of measurement precision and/or accuracy. Apparently, we're to assume that these dimensions could be arrived at by rounding to the nearest km. In that case, they can be taken to have a possible error of ±0.5 km.

The minimum possible area is the product of the minimum possible dimensions: 1.5 km by 4.5 km = 6.75 km².

The maximum possible area is the product of the maximum possible dimensions: 2.5 km by 5.5 km = 13.75 km².

_____

Comment on combining measurement values

You will note that the nominal area is 2 km by 5 km = 10 km², and that the middle value between the minimum and maximum is slightly more than this, at 10.25 km².

It is typically the case that when measurements are combined by operations other than addition and subtraction, the nominal result is different from the middle result in the range of possibilities.

Answer:

E[X] is larger than  E[Y]

E[X]  = 39.283784  and E[Y] = 37

Step-by-step explanation:

Given data

total students = 148

bus 1 students = 40

bus 2 students = 33

bus 3 students = 25

bus 4 students = 50

to find out

E[X] and E[Y]

solution

we know bus have total 148 students and 4 bus

so E[X] is larger than  E[Y] because maximum no of students are likely to chosen to bus and probability of bus is 1/4  as chosen students

and probability  of 40 i.e. P(40)  students = 40/148

P(33) = 33/148

P(25) = 25 / 148

P(50) = 50 / 148

first we find out i.e

E[X]  = 40 P(40) + 33 P(33)+  25 P(25)+  50 P(50)

E[X]  = 40  (40/148) + 33 (33/148)+  25 (25/148)+  50 (50/148)

E[X]  = 39.283784

and

y is bus chosen

E[Y] = 1/4 (40+ 33 + 25 + 50)

so E[Y] = 1/4 (40+ 33 + 25 + 50)

E[Y] = 1/4 (148)

E[Y] = 37

so E[X]  = 39.283784  and E[Y] = 37

The values of E[X] and E[Y] can be calculated by finding the sum of the product of each bus's student count and their respective probabilities. E[X] is expected to be less than E[Y] because students are chosen from each bus inversely proportional to the bus's total students, while for Y, each bus has equal probability of being chosen.

The problem describes an expectation value calculation in the context of probability for two random variables X and Y. X represents a randomly selected student from 148 students who arrived at a stadium in 4 different buses and Y represents a randomly selected bus from the 4 buses and its number of students.

Let's calculate the expected value for X (E[X]) and Y (E[Y]). The expected value of a random variable is computed as a weighted average of the possible outcomes, where each outcome is weighted by its probability. The formula is E(X) = µ = Σ xP(x). Therefore, we need to find the number of students on each bus and their respective probabilities.

For bus 1, we have 40 students, for bus 2, we have 33 students, for bus 3, we have 25 students, and for bus 4, we have 50 students. These numbers represent the possible outcomes for both random variables X and Y. Now, we need to find their respective probabilities, which are determined by the number of students in each bus divided by the total number of students (148).

For X or E[X], the probability of any student being chosen is inversely proportional to the number of students in each bus (since the student is being randomly chosen), while for Y or E[Y], the probability of any bus being chosen is the same (since the bus is being randomly chosen). Therefore, we can expect E[X] to be less than E[Y], as the probability distribution for Y is more weighted towards buses with more students.

To calculate E[Y] and E[X], we follow the expected value formula and multiply each outcome (each bus's number of students) by its probability for both X and Y. So, E[X] is summation over { 40 * ( 40 / 148), 33 * ( 33 / 148), 25 * ( 25 / 148), 50 * ( 50 / 148) } and E[Y] is summation over { 40 * ( 1 / 4), 33 * ( 1 / 4), 25 * ( 1 / 4), 50 * ( 1 / 4) } respectively.

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Answer:

AB= AC times AE/AD

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

In this problem

AB/AC=AE/AD

solve for AB

AB=(AC)(AE)/AD

Answer:

AB= AC times AE/AD

Step-by-step explanation:

AB is on the segment AC, therefore it is proportional to AC .

In order to fulfill the requirement that triangle ABE is a smaller scaled replica of triangle ACD, a scale factor must be applied to the sides of the original figure; in this case, the factor is AE/AD.

Answer:

Answer is in the attachment.

Step-by-step explanation:

To graph x>2 consider first x=2. x=2 is a vertical line and if you want to graph x>2 you need to shade to the right of the vertical line.

To graph x+y<2, I will solve for y first.

x+y<2

Subtract x on both sides:

  y<-x+2

Consider the equation y=-x+2.  This is an equation with y-intercept 2 and slope -1 or -1/1.  So the line you have in that picture looks good for y=-x+2. Now going back to consider y<-x+2 means we want to shade below the line because we had y<.

Now where you see both shadings will be intersection of the shadings and will actually by your answer to system of inequalities you have.  In my picture it is where you have both blue and pink.

I have a graph in the picture that shows the solution.

Also both of your lines will be solid because your question in the picture shows they both have equal signs along with those inequality signs.

Just in case my one graph was confusing, I put a second attachment with just the solution to the system.

Answer:

84=2l+2w

w=21

Step-by-step explanation:

84=2(l+w)

42=l+w

l=42-w

Area=l×w

A=(42-w)×w

Differentiate A=42w-w×w

with respective to "w".

dA/dw= 42-2w

For a minimum or maximum area

dA/dw=0

then, 42-2w=0

w=21

proving "A" is maximum when "w=21"

dA/dw>0 when w<21

dA/dw<0 when w>21

Therefore Area is maximum when "w=21"

The most extensive rectangular garden this man can build with his 84 feet of fencing would be a square with length and width of 21 feet each, yielding a total area of 441 square feet.

A rectangular garden's perimeter can be expressed as P = 2l + 2w, where l is the length and w is the park's width. Given 84 feet of fencing (the total perimeter), this equation becomes 84 = 2l + 2w. Simplified, this gives l + w = 42. Expressing w in terms of l gives w = 42 - l.

Next, breathing, we substitute w into the area formula A = l * w, get A = l * (42 - l). This area expression of one variable forms a quadratic equation, A = -l² + 42l. This suggests that the site is maximized from the quadratic formula when l = -b/2a = 42/2 = 21. So, the length and width of the most significant garden area are both 21 feet, representing a square.

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Answer:

[tex]1.\ \ p(x)\geq0 & \text{ for all values of x.}\\\ 2.\ \sum\ p(x)=1[/tex]

Step-by-step explanation:

There are two requirements for a discrete probability​ distribution that must be satisfied as :-

1. Each probability must be greater than equals to zero.

2. Sum of all probabilities should be equals to 1.

The above conditions are also can be written as :

[tex]1.\ \ p(x)\geq0 & \text{ for all values of x.}\\\ 2.\ \sum\ p(x)=1[/tex]

A discrete probability distribution must satisfy two conditions: each individual outcome probability must be between 0 and 1, and the total of all outcome probabilities must equal to 1.

There are two key requirements that a set of data must meet to be considered a discrete probability distribution:

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we know that θ is in the III Quadrant, and let's recall that on the III Quadrant sine and cosine are both negative, and since tangent = sine/cosine, that means that tangent is positive.  Let's also keep in mind that tan(π) = sin(π)/cos(π) = 0/-1 = 0.

well, the hypotenuse is just a radius unit, so is never negative, since we know sin(θ) = -(5/13), well, the negative number must be the 5, so is really (-5)/13.

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a\implies \stackrel{III~Quadrant}{-12=a} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(\theta )\implies \cfrac{sin(\theta )}{cos(\theta )}\implies \cfrac{~~-\frac{5}{13}~~}{-\frac{12}{13}}\implies -\cfrac{5}{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times -\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{12}\implies \cfrac{5}{12} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(\pi +\theta )=\cfrac{tan(\pi )+tan(\theta )}{1-tan(\pi )tan(\theta )}\implies tan(\pi +\theta )=\cfrac{0+\frac{5}{12}}{1-0\left( \frac{5}{12} \right)} \\\\\\ tan(\pi +\theta )=\cfrac{~~\frac{5}{12}~~}{1}\implies tan(\pi +\theta )=\cfrac{5}{12}[/tex]

The value is 5/12.

To find the value of tan(π + θ) given that θ terminates in Quadrant III and sinθ = -5/13, we need to first note that in the third quadrant, both sine and tangent are negative. Since we already have the value for sine, we can use the Pythagorean identity to find the value for cosine. The identity is sin^2θ + cos^2θ = 1.

Starting with sinθ = -5/13, we square both sides to get sin^2θ = 25/169. Then, we use the Pythagorean identity to solve for cos^2θ which gives us cos^2θ = 1 - 25/169 = 144/169. Taking the positive and negative square root, since cosine is also negative in the third quadrant, we choose the negative root, cosθ = -12/13.

Now, tanθ is the ratio of sine to cosine, which is tanθ = sinθ/cosθ = (-5/13) / (-12/13). This simplifies to tanθ = 5/12. However, the question asks for tan(π + θ), not tanθ. The tangent function has a period of π, so tan(π + θ) = tanθ. Therefore, the answer is 5/12.

Answer:

Explanation:

Correlation is a numerical value that tells how two variables or factors change together.

The correlation between two factors may be positive, negative or nonexistent.

A strong association is shown when the graph of the points representing the factors are reasonably well represented by a line.

A perfect positive correlation is when the two variables are related by a linear function with positive slope (the two factors grow together).

A perfect negative correlation exists when the two factors are related by a linear function with negative slope (one factor grows when the other factor decreases).

A nonexistent correlation is when the two factors are not related in any way to each other and so none function can be obtained.

Final answer:

Correlation measures how two variables are related, with the correlation coefficient indicating the strength and direction of this relationship. The coefficient ranges from -1 to +1, where +1 is a perfect positive correlation and -1 is a perfect negative correlation.

Explanation:

Correlation is a measure of the extent to which two factors are related. Specifically, it refers to how one variable changes in relation to another. The statistical measure used to describe this is called a correlation coefficient, represented by the letter r.

The value of r ranges from -1 to +1, where +1 signifies a perfect positive correlation, -1 signifies a perfect negative correlation, and 0 indicates no correlation at all.

Positive correlation happens when both variables change in the same direction, either increasing or decreasing together. Conversely, a negative correlation indicates that as one variable increases, the other decreases.

While correlation is a useful statistical tool to identify a relationship between two variables, it is crucial to understand that correlation does not imply causation.

This means that just because two variables are correlated, it does not necessarily mean that one variable causes the other to change.

Answer:

∠ZYX = 58°

Step-by-step explanation:

The measure of an inscribed angle or a tangent- chord angle is one half the measure of the intercepted arc.

arc XY is the intercepted arc, hence

∠ZYX = 0.5 × 116° = 58°

Answer: [tex]ZYX=58\°[/tex]

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Tangent\ chord\ Angle=\frac{1}{2}Intercepted\ Arc[/tex]

 In this case you know that for the circle shown in the figure, the arc XY measures 120 degrees, therefore you can find the measure of the angle ZYX. Then you get that the measure of the this angle is the following:

[tex]ZYX=\frac{1}{2}XY\\\\ZYX=\frac{1}{2}(116\°)\\\\ZYX=58\°[/tex]

Answer:

  60 inches

Step-by-step explanation:

Put the given numbers in the formula and solve for the remaining unknown.

  P = 2L +2W

  18 ft = 2L +2×(4 ft)

  10 ft = 2L . . . . . . . . . subtract 8 ft

  5 ft = L . . . . . . . . . . . divide by 2

You want this in inches, so you make use of the fact that each foot is 12 inches.

  5 ft = 5×(12 in) = 60 in

The length of Sarah's fenced yard is 60 inches.

Answer:

60 IN

Step-by-step explanation:

DID THE QUIZ AND GOT IT CORRECT

Answer:

3.58

Step-by-step explanation:

Given :

y = 2x + 4 -------- eq1

y = 2x - 4 -------- eq2

sanity check : both equations have same slope, so we can conclude that they are both parallel to one another.

Step 1: consider equation 1, pick any random x-value and find they corresponding y-value. we pick x = -2

This gives us y = 2(-2) + 4 = 0

Hence we get a point (x,y) = (-2,0)

Step 2: express equation 2 in general form (i.e Ax + By + C = 0)

y = 2x-4 -------rearrange---> 2x - y -4 = 0

Comparing with the general form, we get A = 2, B = -1, C = -4

Recall that the distance between 2 parallel lines is given by the attached formula (see attached picture).

substituting the values for A, B, C and (x, y) from the previous step:

d = | (2)(-2) + (-1)(0) + (-4) |  / √(2² + (-1)²)

d = | -4 + 0 - 4 |  / √(4 + 1)

d = | -8 |  / √5

d = 8  / √5

d = 3.5777

d = 3.58 (rounded 2 dec. pl)

Check the picture below.

For this case we have to define trigonometric relationships in rectangular triangles that the sine of an angle is given by the leg opposite the angle, on the hypotenuse of the triangle.

If we have to:

[tex]Sin A = \frac {3} {5}[/tex]

So:

Leg opposite angle A is: 3

The hypotenuse is: 5

If we apply the Pythagorean theorem, we find the value of the other leg:

[tex]x = \sqrt {5 ^ 2-3 ^ 2}\\x = \sqrt {25-9}\\x = \sqrt {16}\\x = 4[/tex]

So, the Sine of B is given by:

[tex]Sin B = \frac {4} {5}[/tex]

Answer:

[tex]SinB = \frac {4} {5}[/tex]

Answer : The total volume of figure is, [tex]162in^3[/tex]

Step-by-step explanation :

First we have to calculate the volume of cuboid A.

[tex]V_A=l\times b\times h[/tex]

where,

[tex]V_A[/tex] = volume of cuboid A

l = length of cuboid = 9 in

b = breadth of cuboid = 5 in

h = height of cuboid = 2 in

[tex]V_A=9in\times 5in\times 2in[/tex]

[tex]V_A=90in^3[/tex]

Now we have to calculate the volume of cuboid B.

[tex]V_B=l\times b\times h[/tex]

where,

[tex]V_B[/tex] = volume of cuboid B

l = length of cuboid = 9 in

b = breadth of cuboid = 1 in

h = height of cuboid = 2 in

[tex]V_B=9in\times 1in\times 2in[/tex]

[tex]V_B=18in^3[/tex]

Now we have to calculate the volume of cuboid C.

[tex]V_C=l\times b\times h[/tex]

where,

[tex]V_C[/tex] = volume of cuboid C

l = length of cuboid = 9 in

b = breadth of cuboid = 1 in

h = height of cuboid = (8-2=6) in

[tex]V_C=9in\times 1in\times 6in[/tex]

[tex]V_C=54in^3[/tex]

Now we have to calculate the total volume of figure.

Total volume of figure = [tex]V_A+V_B+V_C[/tex]

Total volume of figure = [tex]90in^3+18in^3+54in^3[/tex]

Total volume of figure = [tex]162in^3[/tex]

Thus, the total volume of figure is, [tex]162in^3[/tex]