Write the rule for the translation

Question 9:

cos x = 10/36

Take the inverse on both sides.

arccos(cos x) = arccos(10/36)

x = 73.8723797868

x = 73.87

Question 10:

tan 89 = x

57.2899616308 = x

57.29

Answer:

Step-by-step explanation:

the answer is $22.95

In order to break even store need to charge $22.25 per pair of shorts.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

Fixed cost = $450

Cost of each pair = $11

Number of pairs = 40

So,

The total cost of manufacturing

450 + 11(40) = $890

Now,

Let's say the store charges x per short

Total income = 40x

Now,

At break-even point

The total cost of manufacturing = Total income

890 = 40x

x = $22.25

Hence, In order to break even store need to charge $22.25 per pair of shorts.

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Answer:  Second option.

Step-by-step explanation:

Let be "e" the number of easy puzzles Tina solved and "h"  the number of hard puzzles Tina solved.

Set up a system of equations:

[tex]\left \{ {{e+h=50} \atop {30e+60h=1,950 }} \right.[/tex]

You can use the Eliminationn Method to solve this system of equations:

Therefore, through this proccedure, you get:

[tex]\left \{ {-30e-30h=-1,500} \atop {30e+60h=1,950 }} \right.\\.........................\\30h=450\\\\h=\frac{450}{30} \\\\h=15[/tex]

Tina solved 15 hard puzzles.

Let's assume Tina solved x easy puzzles and y hard puzzles.

Since a player earns 30 points for solving an easy puzzle and 60 points for solving a hard puzzle, the total points Tina earned can be expressed as:

30x + 60y = 1950 (equation 1)

The second piece of information given is that Tina solved a total of 50 puzzles. So, the total number of puzzles can be expressed as:

x + y = 50 (equation 2)

To solve this system of equations, we can use the substitution method. Solve equation 2 for x:

x = 50 - y

Substitute this expression for x in equation 1:

30(50 - y) + 60y = 1950

1500 - 30y + 60y = 1950

30y = 450

y = 15

Therefore, Tina solved 15 hard puzzles.

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Answer: 1000 yards

Step-by-step explanation:

Football field =100 yards

100*10=1000

The answer is 1000 yards

Answer:

$600

Step-by-step explanation:

Answer:

answer to the first question in the image attached above

Step-by-step explanation:

Hope it's helps

Answer:

480

Step-by-step explanation:

This is a problem you can solve by using proportions.  If 32 out of 100 prefer sci-fi, then the ratio representing that looks like this:

[tex]\frac{sci-fi}{total}:\frac{32}{100}[/tex]

Since you have the sci-fi "stuff" on top and the "total number of customers" on the bottom, the next ratio you set up with your unknown needs to follow the same set up.  You are asked how many customers (x) out of 1500 (total number of customers) would prefer sci-fi?  That ratio would look like this in the proportion:

[tex]\frac{sci-fi}{total}:\frac{32}{100}[/tex]×[tex]\frac{x}{1500}[/tex]

Cross multiply to get 100x = 48,000

Solve for x by dividing both sides by 100:

x = 480

Answer: D. 4167 Hertz

Step-by-step explanation:

We know that the formula to calculate frequency by using time period is given by :-

[tex]\nu= \dfrac{1}{T}[/tex], where T is the time period.

We are given that the time period of a musical note :

[tex]T=0.00024\text{ seconds}[/tex]

Then , the frequency of the musical note is given by :-

[tex]\nu= \dfrac{1}{0.00024}=4166.66666667\approx4167\text{ Hertz}[/tex]

Hence, the frequency of the musical note = 4167 Hertz

value will be 46, because absolute value is always positive

Answer:

original price= $150, sale price= $105

Step-by-step explanation:

since it is on sale for 70% of original price, there is 30% off discount.

$45 is 30% of original price (original price is 100%)

1% of original price

= $45 ÷ 30

= $1.50

original price

= $1.50 × 100

=$150

sale price (70% of original price)

= $1.50 × 70

= $105

Final answer:

The original price of the jacket was $150, and after a discount of $45, the sale price is $105.

Explanation:

To find the original price of the jacket when the discount saves $45 and the sale is 70% of the original price, we can set up an equation where the original price is represented by 'P'.

70% of the original price is the same as 0.70P. If this amount is $45 less than the original price, we can express this as:

Original price - Discount = Sale price

P - 0.70P = P(1 - 0.70)

0.30P = $45

To find P, we divide both sides by 0.30:

P = $45 / 0.30

P = $150

Therefore, the original price of the jacket was $150. To calculate the sale price, we subtract the discount of $45 from the original price:

Sale price = Original price - Discount

Sale price = $150 - $45

Sale price = $105

So, the jacket is on sale for $105.

Definition:

A tangent is a line that intersects the circle at one point.

Explanation:

Based on the diagram shown there is one line which intersect the circle once, therefore this statement is true.

Answer

True

Answer:

False

Step-by-step explanation:

The angle between a tangent and the radius of a circle at the point of contact is right.

Thus the triangle formed would be right.

Check using the converse of Pythagoras' identity

If the square on the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.

8² = 64

3² + 7² = 9 + 49 = 58

Since 64 ≠ 58 then the triangle is not right and the line shown is not a tangent.

Answer:

  b = 18

Step-by-step explanation:

From an external point, the products of distances to the near circle intercept and the far circle intercept are the same. For a tangent, such as AC, point A is both the near and far intercept point, so that product is the square of the length of AC.

  (AC)² = (CG)(CV)

  b² = 12·27 = 324 . . . . substitute known values

  b = √324 . . . . . . . . . . take the square root

  b = 18

Answer:

18 is it ;)

Step-by-step explanation:

because it is

The inside dimensions of the living room, taking into account the thickness of the walls, are 12' 1 3/4" x 21' 1 3/4".

To solve this problem, we should subtract the thickness of the walls from the outside dimensions of the living room, as the inside dimensions will be the total length and width minus the thickness of the two opposing walls on each side. The thickness of two walls on one side totals 10 1/4" (since the wall thickness is 5 1/8" per wall) and this total should be subtracted from each outside dimension.

When converting 10 1/4" to feet, the total thickness is approximately 0.852'. Therefore, subtracting this from each dimension gives us:

13' - 0.852' = 12' 1.8" = 12' 1 3/4"

22' - 0.852' = 21' 1.8" = 21' 1 3/4"

Therefore, the correct answer to the question is (A) 12' 1 3/4" x 21' 1 3/4".

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ANSWER

(-2,4)

EXPLANATION

The given equations are:

4x + 5y = 12

7x + 5y = 6

Subtract the first equation from the second equation.

7x-4x+5y-5y=6-12

3x=-6

Divide both sides by 3 to obtain:

x=-2

Put x=-2 into the first equation to get:

4(-2)+5y=12

-8+5y=12

5y=12+8

5y=20

y=20/5

y=4

Checking

4(-2)+5(4)=12

-8+20=12

12=12

Also

7(-2)+5(4)=6

-14+20=6

6=6

Answer:

The solution is (-2,4)

Step-by-step explanation:

* Lets revise how to solve the system of equations algebraically

- If the system of equation is ax+by=c and dx+ey=f, then we can use

 the elimination method to solve

- The steps of the elimination method

# Change the coefficient of one variable in one of the two equation

  to have the same coefficient with opposite sign of this variable in the

  second equation (a = -d)

# Add the two equations to eliminate this variable (by+ey=c+f)

# Solve to find the second variable (y=(c+f)/(b+e))

# Substitute the the value of the second variable in any equation to

  find the first variable

* Now lets solve the problem

∵ 4x+5y=12 ⇒ (1)

∵ 7x+5y=6 ⇒ (2)

- The variable y has the same coefficient in the two equations, then

 eliminate it by multiply one of the equation by -1 to make

 opposite sign

- Multiply equation (2) by -1

∴-7x-5y=-6 ⇒ (3)

- Add (1) and (3)

∴ -3x=6 ⇒ divide both sides by -3

∴ x=-2

- Substitute the value of x in (1) or (2)

∴ 4(-2)+5y=12

∴ -8+5y=12 ⇒ add 8 to both sides

∴ 5y=20 ⇒ divide each side by 5

∴ y = 4

- The solution of the system is the point which has the values of x and y

∴ The solution is (-2,4)

Answer:

Step-by-step explanation:

alright,  lets get started.

Side 5 is opposite.

Side 12 is adjacent.

Side 13 is hypotenuse.

Using SOH CAH TOA,

sin Θ = [tex]\frac{opposite}{hypotenuse}[/tex]

sin Θ = [tex]\frac{5}{13}[/tex]

cos Θ=[tex]\frac{adjacent}{hypotenuse}[/tex]

cos Θ=[tex]\frac{12}{13}[/tex]

tan Θ=[tex]\frac{opposite}{adjacent}[/tex]

tan Θ=[tex]\frac{5}{12}[/tex]   :   Answer

Hope it will help :)

Answer:

Where's the list?

The three consecutive even integers such that the sum of the least integer and the middle integer is 22 more than the greatest integer are 24, 26, and 28.

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Let the first consecutive number be x and the second consecutive number be (x+2).

And the third consecutive number be (x+4).

The sum of the least integer and the middle integer is 22 more than the greatest integer is given by;

x + x  + 2 = 22 + x + 4

2x + 2 = 26 + x

2x - x = 26 - 2

x = 24

The first consecutive number is = x = 24.

And the second consecutive number is = x + 2 = 24 + 2 = 26

And the third consecutive number is = x + 4 = 24 + 4 = 28

Hence, the three consecutive even integers such that the sum of the least integer and the middle integer is 22 more than the greatest integer are 24, 26, and 28.

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Answer:

The rule is [tex]\implies f(n)=4n+1[/tex]

Step-by-step explanation:

The ordered for Larry's inputs and the corresponding outputs displayed by the calculator are:

(1, 5), (2, 9), (3, 13), (4, 17)

We use the y-values of the ordered pairs to obtain the rule.

The y-values are:

[tex]5,9,13,17[/tex]

The y-values form a sequence. The first term of this sequence is:

[tex]a=5[/tex]

The common difference of this sequence is

[tex]d=9-4=5[/tex]

The rule is given by:

[tex]f(n)=a+d(n-1)[/tex]

We substitute the values to obtain:

[tex]f(n)=5+4(n-1)[/tex]

[tex]\implies f(n)=5+4n-4[/tex]

The rule is [tex]\implies f(n)=4n+1[/tex]

Answer:

22 min 13 sec

Step-by-step explanation:

Calculate the following:

      1 clearance                                      1

---------------------------------------- = ---------------------------------  =  22 min 13 sec

1 clearance      1 clearance       1/(50 min)+ 1/(40 min)

------------------ + ------------------

   50 min            40 min

Note:  The LCD here is 200 min.

Also note:  1 / [ 1 / 40 min ] has units "min."

Answer:

It would be:

50 * 40 / (50 + 40) = 2,000 / 90 = 22.222222 minutes

Step-by-step explanation:

Answer:

d. [4 -12 -24 12]

Step-by-step explanation:

This question is on multiplication in matrix

Given matrix B, -4B means -4 × matrix B

     B= [ -1 3 6 -3]

-4B = -4 [-1 3 6 -3]

-4B = [4 -12 -24 12]

Answer:

The second choice down is the one you want

Step-by-step explanation:

There's a couple of things to know about parabolas in this form before you can write the equation from information given.  The first is that if the parabola opens upward or downward it is y = x^2 or y = -x^2.  If it opens to the right or to the left it is a x = y^2 or x = -y^2 parabola.  We can tell how it opens from the location of the focus and what type of directrix it has.  First, a parabola wraps itself around the focus, and the way in which it wraps itself is dependent upon the equation of the directrix.  A "y = " directrix means that the parabola opens up or down (again, it wil wrap itself around the focus) and an "x =" directrix means that the parabola opens to the right or to the left.  Ok.  Now.  Our directrix is a "y =" equation, so the parabola opens either up or down.  If we plot the focus and then draw in the directrix, we see that the focus is above the directrix, so the parabola opens upwards.  

Because of this, the standard form for our parabola is:

[tex](x-h)^2=4p(y-k)[/tex]

where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus, or the vertex and the directrix.  This distance is the same for both.  That means that the vertex lies directly in between the focus and the directrix.  Since our focus is (-5, -1) and the directrix is y = -3, then the vertex lies at a y-coordinate of -1, and will lie on the same x coordinate as does the focus.  So that means our vertex is at (-5, -2).  From this point we see that there is unit that separates it from both the focus and the directrix.  That is our "p" value.  Filling in our equation:

[tex](x+5)^2=4(1)(y+2)[/tex]

which of course simplifies to

[tex](x+5)^2=4(y+2)[/tex]

And there you go!

Answer:

(x+5)2=4(y+2)

Step-by-step explanation:

Answer:

[tex]4,066\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of the bedspread that is red is equal to the area of rectangle minus the area of the circle

step 1

Find the area of rectangle

The area is equal to

[tex]A=72*60=4,320\ in^{2}[/tex]

step 2

Find the area of the circle

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=18/2=9\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(9)^{2}[/tex]

[tex]A=254.34\ in^{2}[/tex]

step 3

Find the area of the bedspread that is red

Find the difference of the areas

[tex]4,320\ in^{2}-254.34\ in^{2}=4,066\ in^{2}[/tex]

Answer:

The mean absolute deviation is 5.952 ⇒ 3rd answer

Step-by-step explanation:

* Lets talk about the mean absolute deviation

- Mean absolute deviation (MAD) of a data set is the average distance

 between each data value and the mean

1- To find the mean absolute deviation of the data, start by finding

   the mean of the data set.

2- Find the sum of the data values, and divide the sum by the

   number of data values.

3- Find the absolute value of the difference between each data value

   and the mean ⇒ |data value – mean|

4- Find the sum of the absolute values of the differences.

5- Divide the sum of the absolute values of the differences by the

   number of data values

* Now lets solve the problem

- The set of data is 31.8 , 22.6 , 13.8 , 16.4 , 28.1

# Find the mean

∵ The mean = sum/ number

∴ The mean = (31.8 + 22.6 + 13.8 + 16.4 + 28.1)/5 = 112.7/5 = 22.54

# Find |data value – mean|

∵ I31.8 - 22.54I = 9.26

∵ I22.6 - 22.54I = 0.06

∵ I13.8 - 22.54I = 8.74

∵ I16.4 - 22.54I = 6.14

∵ I28.1 - 22.54I = 5.56

# Find the sum of the absolute values

∴ The sum = 9.26 + 0.06 + 8.74 + 6.14 + 5.56 = 29.76

# Find the mean absolute deviation

∵ The mean absolute deviation = sum of absolute values/number

∴ The mean absolute deviation = 29.76/5 = 5.952

* The mean absolute deviation is 5.952

Answer:

18.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

Their point of intersection, assuming there is one, will be somewhere on the line y = x.  This line, y = x, is the line of symmetry between a function and its inverse.  So if the two do in fact intersect, it will be at some point on that line

we know that f(1)=2 so f^-1(2)=1

so B is correct!

Answer:  The correct option is

(B) [tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Step-by-step explanation:  We are given to select the correct expression that is the inverse of the following function :

[tex]f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Let y denotes f(x). Then,

[tex]y=f(x)~~~~~~\Rightarrow x=f^{-1}(y).[/tex]

Substituting this value in equation (i), we get

[tex]f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{f^{-1}(y)+1}{f^{-1}(y)}\\\\\\\Rightarrow yf^{-1}(y)=f^{-1}(y)+1\\\\\Rightarrow yf^{-1}(y)-f^{-1}(y)=1\\\\\Rightarrow (y-1)f^{-1}(y)=1\\\\\Rightarrow f^{-1}(y)=\dfrac{1}{y-1}\\\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Thus, the required inverse of the given function is

[tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Option (B) is CORRECT.

Answer:

A)

62/3 = 20.67 hours

B)

60.00 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

0.79370053 is the answer

Answer:

0.125

Step-by-step explanation:

Cube 0.5 to find the value of which 0.5 is the cube root

Working with proper fractions, then

([tex]\frac{1}{2}[/tex])³

= [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex]

and [tex]\frac{1}{8}[/tex] = 0.125

Answer: [tex]300x^{2}[/tex]

Step-by-step explanation: Please see the image below!

The surface area of the composite figure given to us is 300m². Hence option 2 is the right option.

The space enclosed in the given boundary of a 2-D cross-section of a figure is its surface area.

We are asked to find the surface area of the composite figure.

The figure consists of a cube and a pyramid.

The surface area of one face of the cube = a², where a is the length of a side (since its a square)

∴ The surface area of one face = 6² = 36m²

We have 5 faces of the cube, so the total area of the cube is

Area of the cube = 5 * 36m² = 180m².

The surface area of one face of the pyramid = (1/2)*base*height, as it is a triangle.

∴ The surface area of one face = (1/2)*6*10 = 30m²

We have 4 faces of the pyramid, so the total area of the pyramid is

Area of the pyramid = 4*30m² = 120m².

∴ The total surface area of the figure = Area of cube + Area of the pyramid = 180m² + 120² = 300m².

∴ The surface area of the composite figure given to us is 300m². Hence option 2 is the right option.

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Answer:0.76

0.58

Conclusion you are More likely to win by playing regular defense

Step-by-step explanation:

Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Taking the strategy of "regular" defense,

P(winning) = 42

P(losing) = 8

Total regular defense games = 50

Taking the strategy of "prevent" defense,

P(winning) = 35

P(losing) = 15

Total regular prevent games = 50

Total games = 100

Probability of winning when playing regular defense = 42 / 50 = 0.84

Probability of winning when playing prevent defense = 35 / 50 = 0.7

Hence, Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.

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Final answer:

Using Bayes' Theorem, the probability that a person is infected when testing positive and not infected when testing negative can be calculated given the provided probabilities.

Explanation:

(a) Using Bayes' Theorem:

Let A be the event that the person is infected and B be the event that the person tests positive.

From the problem, P(A) = 1/200 (probability of being infected) and P(B|A) = 0.7 (probability of testing positive given infection).

To find P(A|B) (probability of being infected given positive test), we can use Bayes' Theorem: P(A|B) = (P(B|A) × P(A)) / P(B).

P(B) can be calculated using the law of total probability: P(B) = P(B|A) * P(A) + P(B|¬A) × P(¬A), where P(¬A) = 1 - P(A) (probability of not being infected).

From the problem, P(B|¬A) = 0.05 (probability of testing positive given not infected).

Substituting the values, P(B) = (0.7 × 1/200) + (0.05 × 199/200).

Finally, we can calculate P(A|B) = (0.7 × 1/200) / ((0.7 × 1/200) + (0.05 × 199/200)).

(b) Using Bayes' Theorem:

Let A be the event that the person is infected and B be the event that the person tests negative.

Similar to part (a), we can calculate P(B) using the law of total probability: P(B) = P(B|A) × P(A) + P(B|¬A) × P(¬A).

From the problem, P(B|¬A) is the probability of testing negative given not infected, which can be calculated as 1 - P(B|A).

To find P(¬A|B) (probability of not being infected given negative test), we can use Bayes' Theorem: P(¬A|B) = (P(B|¬A) ×P(¬A)) / P(B).

Substituting the values, P(¬A|B) = (P(B|¬A) × (1 - P(A))) / P(B).