A survey of 25 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $65.00 per hour. The sample standard deviation was $6.25 per hour.

Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Using sine rule, the value of B in the triangle is 53.13°

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other. The other names of the law of sines are sine law, sine rule and sine formula

The law of sine is explained in detail as follow:

In a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.

Mathematically, this can be represented as;

a / sin A = b / sin B = c / sin C

In this question given;

a = 400, b = 300, A = 2θ, B = θ

Using sine law;

a / sin A = b / sin B

400 / sin (2θ) = 300 / sin θ

400 / sinθcosθ = 300 / sinθ

400 / tanθ = 300

tan θ = 4/3

θ = tan⁻¹(4/3)

θ = 53.13°

The value of B is 53.13°

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Answer:

B, C, G

Step-by-step explanation:

If we look at the graph, it shows that if an employee works for 5 hours, then they will earn $36.25.

We can take 36.25 and divide that by 5 to get the hourly wage.

36.25 ÷ 5 = 7.25

We now know that employees get $7.25 every hour.

Using this we can look back to the graph.

'A' says that if an employee does not work, they will earn $7.25.

We know that this is wrong because if you do not work, then you do not earn money.

Let's look at 'B'.

If employees work for one hour, they will earn $7.25

We know this is correct because we now know the hourly wage.

Let's look at 'C'

If employees work for 4 hours, then they will get a revenue of $29.

We can figure this out by using this equation.

number of hours × hourly wage = total payment

4 × 7.25 = 29

Then this means that this is correct.

Let's look at 'D'

It says that if employees work for 10 hours, they will earn $73

Let's use that same equation again.

10 × 7.25 = 72.5

Employees earn $72.5 for working 10 hours, not $73.

So, this is obviously incorrect.

Let's look at 'E'

It says that if employees work for 3.5 hours, they will get a revenue of $21.75.

3.5 × 7.25 = 25.375

Therefore, this is incorrect.

Now let's take a look at 'F'.

It says that if employees work for 7.25 hours, then they earn $1.

This is incorrect.

And lastly, 'G'.

We know that if you do not work, then you do not earn money.

Therefore, A, B and G are the correct answers.

Answer:

B. y=1/4x+2

Step-by-step explanation:

Equation of a Line

We are given a graph and we must select which of the proposed equations corresponds with the graph.

Let's identify two clear points in the graph. They are (0,2) and (4,3)

Substituting x=0 in the correct equation should give y=2. All the equations but C. give y=2 when x=0

Now when x=4, y should be 3.

Substituting in the each equation:

y=4x+2 = 4*4+2=18

y=1/4(4)+2=3

y=3x+2=3*4+2=14

The only equation that passes through both points is:

B. y=1/4x+2

Answer:

The equation best represents the relationship  between x and y in the graph is:

y =1/4x + 2

Hence, option B is correct.

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where

Taking two points from the given graph

Determining the slope between (0, 2) and (4, 3)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [3 - 2] / [4 - 0]

               = 1 / 4            

Thus, the slope of the line = m = 1/4

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 2

Thus, the y-intercept b = 2

now substituting m = 1/4 and b = 2

y = mx+b

y =1/4x + 2

Therefore, the equation best represents the relationship  between x and y in the graph is:

y =1/4x + 2

Hence, option B is correct.

Answer:

Do I calculate the area?

Step-by-step explanation:

Answer:

sept one

Step-by-step explanation:

The two ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20).

Given the coordinates of mid point be (4,-10).

We are required to find the ordered pairs that the mid point is (4,-20).

Coordinates show positions of points or something else on a surface.

There are various combinations whose mid point is (4,-10).

First are (4,-20),(4,0).

Mid point =[(4+4)/2,(-20+0)/2]

=(4,-10)

Second are (4,0) , (4,-20)

Mid point=[(4+4)/2,(0-20)/2]

=(4,-10)

Third are (8,-20),(0,0)

Mid point=[(8+0)/2,(-20+0)/2]

=(4,-10)

Fourth are (0,-20),(8,0)

Mid point =[(0+8)/2,(-10+0)/2]

=(4,-10)

Hence the ordered pairs that the mid point is (4,-10) are (4,-20),(4,0) & (4,0),(4,-20)& (8,-20),(0,0)&(0,-20),(8,0)&(0,0),(8,-20).etc.

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so we have a point at -2-i or -2 - 1i, that means that both "x" and "y" are negative, the only occurs in the III Quadrant, so hmmm let's find the modulus and angle θ

\(\stackrel{a}{-2}\stackrel{b}{-1i}\hspace{5em} \begin{cases} r=\sqrt{(-2)^2 + (-1)^2}\\ \qquad \sqrt{5}\\ \theta =tan^{-1}\left( \frac{-1}{-2} \right)\\[1em] \qquad \approx 206.57^o \end{cases} \\\\\\ \stackrel{\textit{let's keep in mind that}}{\sqrt[3]{\sqrt{5}}\implies \left( 5^{\frac{1}{2}} \right)^{\frac{1}{3}}}\implies 5^{\frac{1}{6}}\implies \sqrt[6]{5} \\\\[-0.35em] ~\dotfill\)

\(\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\boxed{k=0}\hspace{5em} \sqrt[ 3 ]{\sqrt{5}} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o }{3} \right) +i \sin\left( \cfrac{ 206.57^o }{3} \right)\right] \\\\\\ \sqrt[6]{5}\left[ \cos(68.86^o) +i \sin(68.86^o)\right] ~~ \approx ~~ 0.47~~ + ~~1.22i \\\\[-0.35em] ~\dotfill\)

\(\boxed{k=1}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 566.57^o }{3} \right) +i \sin\left( \cfrac{ 566.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(188.86^o) +i \sin(188.86^o)\right] ~~ \approx ~~ -1.29~~ - ~~0.20i \\\\[-0.35em] ~\dotfill\)

\(\boxed{k=2}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 926.57^o }{3} \right) +i \sin\left( \cfrac{ 926.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(308.86^o) +i \sin(308.86^o)\right] ~~ \approx ~~ 0.82~~ - ~~1.02i\)

just a quick clarification, notice that if we get the inverse tangent of (-1 / -2) the angle we get will be in the range of ±π/2, that's because that is the range inverse tangent is restricted to, however, our terminal point on the complex plane is on the III Quadrant, not the 1st one, so we use the reference angle on the III Quadrant, and that is about 206.57°.

Answer:

x = \(\sqrt{165}\)

Step-by-step explanation:

Pythagorean Theorm: a^2 + b^2 = c^2

a^2 + b^2 = c^2

14^2 + x^2 = 19^2

196 + x^2 = 361

x^2 = 165

x = \(\sqrt{165}\)

Dividing by a fraction is equivalent to multiply by its inverse. For example, if you want to divide 3/4 by 5/6, you have to compute 3/4 multiplied by 6/5

18/20 can be simplified by dividing each term by the same number, in this case by 2.

If you want to divide mixed numbers, first, you have to convert the mixed numbers into improper fractions, and then proceed as explained above.

The length of the third side is 2√34 + 6.

We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. Then we have:

2√34 + 6 > x

Subtracting 6 from both sides, we get:

2√34 > x - 6

Adding 6 to both sides, we get:

x < 2√34 + 6

Therefore, the length of the third side must be less than 2√34 + 6.

To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:

2√34 + 6 = x

If this is true, then the given sides can form a triangle.

Simplifying the equation, we get:

x = 2√34 + 6

The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.

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Answer:

180

Step-by-step explanation:

180

Got it correct

Answer: No solutions

Step-by-step explanation:

\(5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9\)

However, as absolute value is non-negative, there are no solutions.

Using the distance between a point and a line and the conversion of the units to yards, it is found that the minimum distance from the giant pumpkin is of  8.9 yards.

Suppose that we have a linear function defined according to the following rule, in standard notation:

Ax + By + C = 0.

And a point with coordinates given by:

P(x*,y*)

The shortest distance between the line and the point is given by:

\(d = \frac{|Ax^\ast + By^\ast + C|}{\sqrt{A^2 + B^2}}\)

The line of the path in this problem has:

Hence:

y = 0.5x.

-0.5x + y = 0

-x + 2y = 0.

The coefficients are:

A = -1, B = 2.

The giant pumpkin has coordinates given by:

(x*, y*) = (-4, -3).

Hence the distance in units is given by:

d = |(-1)(-4) + 2(-3)|/sqrt(5)

d = 2/sqrt(5)

d = 0.89 units.

Each unit is equivalent to 10 yards, hence the shortest distance in yards is given by:

0.89 x 10 = 8.9 yards.

The problem is given by the image at the end of the answer.

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Answer:

30

Step-by-step explanation:

3(6-4)*5= 3*2*5=30

The inequality 4x - 2y < 12 is represented by the attached graph. which is the answer would be an option (B).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per option (B),

4x - 2y < 12

We can see that the x-intercept is (0, -6), and the y-intercept is (2.5, 0) in the given graph which is determined by substituting the value of x and y is equal to 0 in the equation 4x - 2y = 12.

The inequality 4x - 2y < 12 is represented by the attached graph.

Hence, the answer would be option (B).

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Answer:

1. B

2. C

3. B

Step-by-step explanation:

You're Welcome

i think its a because i estimated

Answer:

neither

Step-by-step explanation:

parallel lines will have the same number next to the x

perpendicular lines will have the negative reciprocal number next to the x

(for example 2 and -1/2 are negative reciprocals)

y−4=3(x+5)

parenthesis first

y−4=3x+15

y=3x+19

y+3= −13(x+1)

y+3= −13x−13

y= −13x−16

3x and −13x are neither the same nor negative reciprocals of each other so

the answer is neither

The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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A has fixed one time fee of $12 and if you go to it say "m" months you pay $28 for each month, so your total cost at A is really 12 + 28m.

B has a fixed one time fee of $20 and if you go to it "m" months you pay $26 for each month, so you total cost at B is 20 + 26m.

how many months for the cost to be the same?

\(\stackrel{A}{12+28m}=\stackrel{B}{20+26m}\implies 12+2m=20\implies 2m=8\implies m=\cfrac{8}{2}\implies m=4\)

well, since the cost for both is the same, we can just get A's, knowing that B is the same

\(12+28(4)\implies 12+112\implies 124\)

Answer:

I had this question and i got it right it is the measure is four

Step-by-step explanation:

Answer: con que cariño?

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

Rewrite the root be,

\(\sqrt{39}=\sqrt{3\cdot13}=\sqrt{3}\sqrt{13}\)

We know that \(\sqrt{3}\approx1.7,\sqrt{13}\approx3.6\)

Write decimals as fractions and multiply them,

\(\frac{17}{10}\cdot\frac{36}{10}=\frac{612}{100}=6.12\)

So it should be on somewhere around the next tick from 6.

Hope this helps :)

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Step-by-step explanation:

Given equation is:-

Dividing both sides by 4, we get

By doing simply, we get

Hence, the value of c will be ¾.

Answer:

See proof below

Step-by-step explanation:

Important points

Onto

For a function with a given co-domain to be "onto," every element of the co-domain must be an element of the range.

However, the co-domain here is suggested to be \(\mathbb R\), whereas the range of f is not \(\mathbb R\) (proof below).

Proof (contradiction)

Suppose that f is onto \(\mathbb R\).

Consider the output 7 (a specific element of \(\mathbb R\)).

Since f is onto \(\mathbb R\), there must exist some input from the domain \(\mathbb R\), "p", such that f(p) = 7.

Substitute and solve to find values for "p".

\(f(x)=-3x^2+4\\f(p)=-3(p)^2+4\\7=-3p^2+4\\3=-3p^2\\-1=p^2\)

Next, apply the square root property:

\(\pm \sqrt{-1} =\sqrt{p^2}\)

By definition, \(\sqrt{-1} =i\), so

\(i=p \text{ or } -i =p\)

By the Fundamental Theorem of Algebra, any polynomial of degree n with complex coefficients, has exactly n complex roots.  Since the degree of f is 2, there are exactly 2 roots, and we've found them both, so we've found all of them.

However, neither \(i\)  nor \(-i\) are in \(\mathbb R\), so there are zero values of p in \(\mathbb R\) for which f(p)= 7, which is a contradiction.

Therefore, the contradiction supposition must be false, proving that f is not onto \(\mathbb R\)