Determine the principal value of the function: Arc sin(square root of 3/2)

Answer:

The answer in the procedure

Step-by-step explanation:

case 1) If the function is

[tex]y=2\sqrt{x-6}[/tex]

we know that

The term in the radicand must be positive

so

[tex]x-6\geq 0\\ \\x\geq 6[/tex]

therefore

The domain of the function is the interval -----> [6,∞)

All real numbers greater than or equal to 6

case 2) If the function is

[tex]y=2\sqrt{x}-6[/tex]

we know that

The term in the radicand must be positive

so

[tex]x\geq 0[/tex]

therefore

The domain of the function is the interval -----> [0,∞)

All real numbers greater than or equal to 0

Answer:

x = 34

Step-by-step explanation:

The 3 given angles form a straight angle and sum to 180°, hence

x + 12 + 100 + x = 180

2x + 112 = 180 ( subtract 112 from both sides )

2x = 68 ( divide both sides by 2 )

x = 34

Answer:

x=34

Step-by-step explanation:

Alright.

x+12+100+x=180

         2x+112=180

                2x=68

                   x=34

The formula for the area of a rectangle is...

Area = length x width

A = L x W

What we know so far...

Area is 590 cm^2

length is 12 cm

width is unknown

Plug all of these into the equation for area of a rectangle:

590 = 12 * w

or

590 = 12w

Letter A is the correct answer

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

  3) (1, 0)

Step-by-step explanation:

The midpoint can be computed as the average of the coordinates.

  M = (A + D)/2 = ((-2, 2) +(4, -2))/2 = ((-2+4)/2, (2-2)/2) = (1, 0)

The midpoint is (1, 0).

___

This is also easily seen on a graph of the points.

Answer:

[tex]2x + 50,000 \ge 70,000[/tex].

[tex]x \ge 10,000[/tex].

Step-by-step explanation:

What's the total income of Ms. Wolf in a year?

The annual income of Ms. Wolf comes in two parts:

How many commission does Ms. Wolf receive for each share she sold? [tex]\$\;50 \times 4\% = \$\;50 \times 0.04 = \$\;2[/tex].

Let the number of shares that Ms. Wolf sold be [tex]x[/tex]. Ms. Wolf will receive a commission of [tex]\$\;2x[/tex].

Total annual income of Ms. Wolf: [tex]\$\; (50,000 + 2x)[/tex].

The phrase "at least" indicates that [tex]\$\; (50,000 + 2x)[/tex] shall be greater than or equal to $70,000. That is:

[tex]\$\; (50,000 + 2x)\ge \$\;70,000[/tex].

[tex]2x + 50,000 \ge 70,000[/tex].

[tex]x \ge 20,000[/tex].

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}}~\hfill \stackrel{mixed}{1\frac{5}{8}\implies \cfrac{1\cdot 8+5}{8}}\implies \stackrel{improper}{\cfrac{13}{8}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{total salad}}{\cfrac{13}{2}}\div \stackrel{\stackrel{\textit{conainer's}}{\textit{capacity}}}{\cfrac{13}{8}}\implies \cfrac{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\underset{1}{\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\cdot \cfrac{\stackrel{4}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies 4[/tex]

The green square is 15 ft wide by 15 ft tall.

The area of one green square is 15 x 15 = 225 square feet.

There are 4 sides plus the base : 225 x 5 = 1125 square feet for the green part.

One triangle has a base 15 feet wide and a height of 9 feet.

The area for one triangle is 1/2 x 15 x 9 = 67.5 square feet.

There are 4 triangles: 67.5 x 4 = 270 square feet.

Total: 1125 + 270 = 1,395 square feet.

Answer:

The correct answer is B. The number of rides and the total cost are both dependent variables, as both depend on the amount of money that Nia has.

Step-by-step explanation:

Both the number of rides and the total cost are variables that depend on the amount of money that Nia has. This is so because the passage has a cost, and that cost can not exceed the amount of money that Nia has, because if she exceeds her $ 19.50 she won't be able to pay the ticket. Then, Nia has a possible amount of 26 rides as maximum (19.5 / 0.75 = 26), and the maximum total cost that can be paid is $ 19.50.

Final answer:

The correct answer is: C) The number of rides is the independent variable, and the total cost is the dependent variable.

Explanation:

In the scenario where Nia has $19.50 to ride the subway around New York, at a cost of $0.75 per ride, the correct identification of the dependent and independent variables is crucial for understanding the relationship between these quantities.

The independent variable is the number of rides Nia can take. This is because it is the variable over which we have control or can set at different levels; in other words, Nia decides how many trips she takes.

The dependent variable is the total cost of these rides. The cost depends on how many rides she takes, changing accordingly with that number.

Therefore, the correct answer is: C) The number of rides is the independent variable, and the total cost is the dependent variable.

Answer:

B.38

Step-by-step explanation:

Answer: Option D

Step-by-step explanation:

By definition if we have a function F (x) and perform a transformation of the form

[tex]G (x) = F (x + c)[/tex]

Then it is true that:

If c is negative the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the right

If c is positive, the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the left.

Note that in this case the transformation is:

[tex]G (x) = F (x + 9)[/tex]

Then [tex]c = 9[/tex] and [tex]c> 0[/tex]

Therefore the graph of G(x) will be equal to the graph of F(x) displaced horizontally 9 units to the left

The answer is the option D.

ANSWER

D. The graph of G(x) is the graph of F(x) shifted 9 units to the left.

EXPLANATION

The given functions are F(x) and G(x).

The function, G(x) is obtain by translating or shifting the graph of F(x).

This translation is of the form.

[tex]G(x) = F(x+ 9)[/tex]

The '+9' within the parenthesis tells us that the shift is 9 units to the left.

Remember that for horizontal shift:

+ means a shift to the left.

The correct answer is D.

Answer:

18%

Step-by-step explanation:

From the table you can state that:

Use the definition of the probability

[tex]Pr=\dfrac{\text{The number of favorable outcomes}}{\text{The number of all possible outcomes}}[/tex]

So,

Hence, the probability is

[tex]Pr=\dfrac{1,879}{10,730}\approx 0.1751\approx 18\%[/tex]

The answers are:

[tex]MaximumDistance=1200.1ft\\MinimumDistance=1199.9ft[/tex]

Since we are given the margin of error and it's equal to ±0.1 feet, and we know the surveyed distance, we can calculate the maximum and minimum distance. We must remember that margin of errors usually involves and maximum and minimum margin of a measure, and it means that the real measure will not be greater or less than the values located at the margins.

We know that the surveyed distance is 1200 feet with a margin of error of ±0.1 feet, so, we can calculate the maximum and minimum distances that the reader could assume in the following way:

[tex]MaximumDistance=ActualDistance+0.1feet\\\\MaximumDistance=1200feet+0.1feet=1200.1feet[/tex]

[tex]MinimumDistance=ActualDistance-0.1feet\\\\MaximumDistance=1200feet-0.1feet=1199.9feet[/tex]

Have a nice day!

Answer:a or b

Step-by-step explanation:

Answer:

B. 3 sqrt 2

Step-by-step explanation:

got oit right on edge

Answer:

.5b

Step-by-step explanation:

( .125 b^3) ^ 1/3

We know that ( xy) ^c = x^c  * y ^c

( .125) ^ 1/3   (b^3) ^ 1/3

Rewriting .125 as .5^3

( .5^3) ^1/3 ( b^3) ^ 1/3

We know that a^c^d = a^(c*d)

.5 ^ (3*1/3)   b ^ (3*1/3)

.5 b

[tex]\dfrac{a^2}{b}[/tex] is an integer, where [tex]a,b\in\mathbb{Z_+}[/tex], therefore [tex]b|a^2[/tex] and [tex]b\leq a^2[/tex]

[tex]a=pq[/tex] therefore [tex]a^2=p^2q^2[/tex]

[tex]b>a\wedge b\leq a^2[/tex], therefore [tex]pq<b\leq p^2q^2[/tex]

So,

[tex]b\in\{p^2q,pq^2,p^2q^2\} \\|\{p^2q,pq^2,p^2q^2\}|=3 \implies \text{B}[/tex]

For this case we have to:

n: It's the variable that represents the number of lawns that mowed Wally last week.

If you tell us as a fact that this week Wally mowed two more lawns, then we have the following expression:

[tex]n + 2[/tex]

Finally, the expression is:

[tex]n + 2[/tex]

Answer:

[tex]n + 2[/tex]

Option A

Answer:

A.f(n) = f(n − 1) + 4

Step-by-step explanation:

4+4 = 8

8+4 = 12

We are adding 4 to the term  before it

f(n) = f(n-1) +4

Answer: A.f(n) = f(n − 1) + 4 Hope this helps :)

Answer:

$27410

Step-by-step explanation:

Duane is filing his federal income tax return with the 1040EZ form using the Single filing status, and nobody can claim him as a dependent. If he had wages, salaries, and tips of $37,400, taxable interest of $160, and no unemployment compensation, what should he enter on line 6 of the Income section below?

form 1040EZ is the form used for paying tax by the Inland Revenue Services(IRS)

Line 6 of the 1040EZ  from will contain taxable income

so he will fill

$27410

His taxable income is when standard deductions and deductions for exemption is subtracted from the total income

37,400+160-(6200+3950)

$27410

1040EZ form

Filing status and income:,

Filing status: Single

Are you someone's dependent?:  No

Wages, salaries, tips, etc:

$37,400

Taxable interest:

$160

Unemployment compensation:

$0

Standard deduction:

$6,200

Deduction for exemptions:

$3,950

Taxable income:

$27,410

Federal income tax withheld:

$0

Answer:

28,210

Step-by-step explanation:

just answered it

Answer:

Part 1) [tex]y=-x^{2}[/tex]  ---> Translated up by 1 units

Part 2) [tex]y=x^{2}+1[/tex]  ---> Reflected across the x-axis

Part 3) [tex]y=-(x+1)^{2}-1[/tex]  ---> Translated left by 1 unit

Part 4) [tex]y=-(x-1)^{2}-1[/tex] ----> Translated right by 1 unit

Part 5) [tex]y=-x^{2}-1[/tex]  ----> Reflected across the y-axis

Part 6) [tex]y=-x^{2}-2[/tex]  ----> Translated down by 1 unit

Step-by-step explanation:

we know that

The parent function is

[tex]y=-x^{2}-1[/tex] ----> this is a vertical parabola open downward with vertex at (0,-1)

Calculate each case

Part 1) Translated up by 1 unit

The rule of the translation is

(x,y) -----> (x,y+1)

so

(0,-1) ----> (0,-1+1)

(0,1) ----> (0,0) ----> the new vertex

The new function is equal to

[tex]y=-x^{2}[/tex]

Part 2) Reflected across the x-axis

The rule of the reflection is

(x,y) -----> (x,-y)

so

(0,-1) ----> (0,1) ----> the new vertex

The new function is equal to

[tex]y=x^{2}+1[/tex]

Part 3) Translated left by 1 unit

The rule of the translation is

(x,y) -----> (x-1,y)

so

(0,-1) ----> (0-1,-1)

(0,1) ----> (-1,-1) ----> the new vertex

The new function is equal to

[tex]y=-(x+1)^{2}-1[/tex]

Part 4) Translated right by 1 unit

The rule of the translation is

(x,y) -----> (x+1,y)

so

(0,-1) ----> (0+1,-1)

(0,1) ----> (1,-1) ----> the new vertex

The new function is equal to

[tex]y=-(x-1)^{2}-1[/tex]

Part 5) Reflected across the y-axis

The rule of the reflection is

(x,y) -----> (-x,y)

so

(0,-1) ----> (0,-1) ----> the new vertex

The new function is equal to

[tex]y=-x^{2}-1[/tex]

Part 6) Translated down by 1 unit

The rule of the translation is

(x,y) -----> (x,y-1)

so

(0,-1) ----> (0,-1-1)

(0,1) ----> (0,-2) ----> the new vertex

The new function is equal to

[tex]y=-x^{2}-2[/tex]

Answer:

7

Step-by-step explanation:

7 x 3 = 21

Answer:

Cost of yard silk fabric : $35

Cost of yard of woolen fabric: $60

Step-by-step explanation:

This problem must be represented as a linear system of equations

Let

x = the cost of 1 yard of woolen fabric

y = the cost of 1 yard of silk fabric

The problem tells us

4 yards of woolen fabric costs $30.00 more than 6 yards of silk fabric.

4.x = 6.y + 30

cost of the silk is $25.00 less than the cost of the wool

y = x - 25

The system of equations is

4x - 6y =  30

x - y  = 25

If we solve this system of equations using a calculator or computational tool, we get the following values

x = $60

y = $35

Answer:

x=225

Step-by-step explanation:

\sqrt{x} + (-13 + 13) = 2 + 13

\sqrt{x} = 15

√x-13=2

x=225

If you meant to write...

[tex]\sqrt{x - 13} = 2[/tex]

Then the following is the answer:

To solve this you must get rid of the square root. The opposite of square root is square. You must square both sides since what you do to one side you must do to the other...

([tex]\sqrt{x-13} )^{2}[/tex] = [tex]2^{2}[/tex]

x - 13 = 4

Finish completely isolating x. To do this first add 13 to both sides (what you do on one side you must do to the other). Since 13 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

x + (-13 + 13) = 4 + 13

x + 0 = 17

x = 17

If you meant to write...

[tex]\sqrt{x}[/tex] - 13 = 2

Then the following is the answer:

To isolate [tex]\sqrt{x}[/tex]. To do this first add 13 to both sides (what you do on one side you must do to the other). Since 13 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

[tex]\sqrt{x}[/tex] + (-13 + 13) = 2 + 13

[tex]\sqrt{x}[/tex] = 15

To completely isolate x you must get rid of the square root. The opposite of square root is square. You must square both sides since what you do to one side you must do to the other...

[tex](\sqrt{x})^{2} = 15^{2}[/tex]

x = 225

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

13/18

Step-by-step explanation:

We need to get a common denominator for 9,6,3

That would be 18

5/9 *2/2 = 10/18

5/6 * 3/3 = 15/18

2/3 *6/6 = 12/18

5/9+5/6 = 10/18 +15/18 = 25/18

Then

25/18 - 2/3 = 25/18 - 12/18 = 13/18

Answer:

Option 2  

Step-by-step explanation:

Given : Equation [tex]\log_2(3x-1)=2[/tex]

To find : Which graph shows the solution to the equation?

Solution :

First we distribute the equation into two equation.

Let  Equation 1 be [tex]y=\log_2(3x-1)[/tex]

and Equation 2 be [tex]y=2[/tex]

Plot these two equation,

The equation 1 with purple line and equation 2 with orange line.

As these equation are equal there intersection point is given by,

Intersection point (1.667,2)

From the given graph only option 2 gives the correxct intersection point.

So, option 2 is correct.

Refer the attached figures below.  

Answer:

graph 2

Step-by-step explanation:

edg '23

Answer:

The best estimate for the solution is the point (0.5,-3.5)

Step-by-step explanation:

we have

-----> equation A

-----> equation B

we know that

The solution of the system of equations is the intersection point both graphs

Using a graphing tool

The intersection point is

see the attached figure

therefore

The solution of the system of equations is the point

The best estimate for the solution is the point

Answer:

  6 yards by 11 yards

Step-by-step explanation:

Factors of 66 are ...

  66 = 1·66 = 2·33 = 3·22 = 6·11

The last pair of factors differ by 5, so represent the solution to the problem.

The width of the parking lot is 6 yards; the length is 11 yards.

Final answer:

The parking lot's dimensions are found by setting a quadratic equation w × (w + 5) = 66 based on its area. Solving for w, the width is 6 yards, hence the length is 11 yards, making the dimensions 6 yards by 11 yards.

Explanation:

To find the dimensions of the parking lot when the length is 5 yards more than the width and the area is 66 square yards, we can set up an equation based on the area of a rectangle (area = length × width). We can define the width as w and the length as w + 5 since the length is 5 yards more than the width.

The equation representing the area will then be:

w × (w + 5) = 66

Solving this quadratic equation (w^2 + 5w - 66 = 0) by factoring or using the quadratic formula, we find that w = 6 or w = -11. We discard the negative value since a width cannot be negative, so the width is 6 yards and the length is 11 yards (since it's 5 yards more than the width).

Therefore, the dimensions of the parking lot are 6 yards by 11 yards.

Answer:

x = 3.1 ft

Step-by-step explanation:

Use Pythagoras' Theorem to find the base of the triangle. The base of the triangle is half of 'x'. Let's call the base 'y' for now.

To find 'y' we must use this formula,

[tex]y^{2} = c^{2} -b^{2}[/tex]

'c' is the hypotenuse, the longer side, and 'b' is the other short side.

Sub in the numbers for 'c' and 'b',

[tex]y^{2} = 2.1^{2} -1.4^{2}[/tex]

               = 2.45

Square root both sides to get 'y' by itself,

y = 1.5652.....

Remember that 'y' is half of x? Simply multiply 'y' by 2 to get an answer for 'x',

x = 1.5652.... x 2

  = 3.1 ft (1 d.p. nearest tenth)

Hope this helped!!

Answer:

All events are independent

Step-by-step explanation:

You are given the table

[tex]\begin{array}{cccc}&\text{Chocolate}&\text{Vanilla}&\text{Total}\\\text{Adults}&0.21&0.39&0.60\\\text{Children}&0.14&0.26&0.40\\\text{Total}&0.35&0.65&1.00\end{array}[/tex]

Two events A and B are independent when

[tex]Pr(A\cap B)=Pr(A)\cdot Pr(B)[/tex]

a) A="Chocolate"

B="Adults"

A and B="Chocolate and Adults"

[tex]Pr(A)=0.35\\ \\Pr(B)=0.60\\ \\Pr(A\cap B)=0.21[/tex]

Since [tex]0.35\cdot 0.60=0.21[/tex] events are independent

b) A="Children"

B="Chocolate"

A and B="Children and Chocolate"

[tex]Pr(A)=0.40\\ \\Pr(B)=0.35\\ \\Pr(A\cap B)=0.14[/tex]

Since [tex]0.40\cdot 0.35=0.14[/tex] events are independent

c) A="Vanilla"

B="Children"

A and B="Vanilla and Children"

[tex]Pr(A)=0.65\\ \\Pr(B)=0.40\\ \\Pr(A\cap B)=0.26[/tex]

Since [tex]0.65\cdot 0.40=0.26[/tex] events are independent

Answer:

5 but its probaly not right bc im just looking for pointsStep-by-step explanation:

Area of a triangle = height x base ÷ 2

When ever you have an isosceles triangle, remember that you can split it in half to form two right angled triangles - which allow you to use Pythagoras' Theorem.

So we split 10cm in half to get 5cm.

We can then use 13cm and 5cm to work out the height:

Height = √(13²  - 5²)      (Note: you subtract because you are using the    

           = √144              (hypotenuse)

           =  12

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

Now to get the area, we just multiply the base (which is 10) by the height (which is 12) and divide by 2:

Area = 12 x 10 ÷ 2

        = 6 x 10               (note: 12 ÷ 2 = 6 )

        = 60 cm²

_____________________________________

Answer:

60 cm²