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Answer:

x = 73.3

y = 46.2

Step-by-step explanation:

Reference angle (θ) = 39°

Adjacent = 57

Hypotenuse = x

Opposite = y

Recall: SOHCAHTOA

✔️To find x, apply CAH:

Cos θ = Adjacent/Hypotenuse

Plug in the values

Cos 39° = 57/x

x × Cos 39° = 57

x = 57/Cos 39°

x = 73.3 (nearest tenth)

✔️To find x, apply TOA:

Tan θ = Opposite/Adjacent

Plug in the values

Tan 39° = y/57

57 × Tan 39° = y

y = 46.2 (nearest tenth)

Answer

1/2

Step-by-step explanation:

Answer:

71 in²

Step-by-step explanation:

surface area = (4×6)+(2×½×4×5)+(2×½×6×4.5)

= 24+20+27 = 71 in²

Answer:

Volume of rectangular prism = 10/9 inch³

Step-by-step explanation:

Given:

Size of each cube = 1/3 inch

Find:

Volume of rectangular prism

Computation:

Length of rectangular prism = 2 x [1/3]

Length of rectangular prism = 2/3 inch

Width of rectangular prism = 3 x [1/3]

Width of rectangular prism = 3/3

Width of rectangular prism = 1 inch

Height of rectangular prism = 5 x [1/3]

Height of rectangular prism = 5/3 inch

Volume of rectangular prism = Length x Width X Height

Volume of rectangular prism = [2/3] x [1] x [5/3]

Volume of rectangular prism = 10/9 inch³

The average monthly wage for the entire workforce of the business is $7489.09.

The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.

Given, The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have equal monthly salaries of $7200, $7600, $6900, $8200, $7800, and $7400 respectively.

First, calculate the total monthly salary

22*7200 + 32*7600 + 18*6900 + 16*8200 + 10*7800 + 12*7200  dollars.

Total monthly salary = $823,800

Then divide this sum by the total number of employees  

 22 + 32 + 18 + 16 + 10 + 12

Total number of employees = 110

the mean monthly salary of all the employees  = [tex]\frac{Total salary}{total number of employee}[/tex]

the mean monthly salary of all the employees  = 823800/ 110

the mean monthly salary of all the employees = 7489.0909

Therefore, the mean monthly salary of all the employees of the company is $7489.09.

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Answer:

degree 24.7

Radian 0.43

Step-by-step explanation:

Given:

Radius of the circle = 6 inches

Central angle = 75 degrees.

To find:

The length of subtended arc, i.e., x.

Solution:

The formula for arc length is:

[tex]s=2\pi r\times \dfrac{\theta}{360^\circ}[/tex]

Where, r is the radius and [tex]\theta [/tex] is the central angle.

Putting [tex]s=x, r=6, \pi=3.14, \theta =75^\circ[/tex] in the above formula, we get

[tex]x=2(3.14)(6)\times \dfrac{75^\circ}{360^\circ}[/tex]

[tex]x=2(3.14)(6)\times \dfrac{5}{24}[/tex]

[tex]x=7.85[/tex]

[tex]x\approx 7.9[/tex]

Therefore, the value of x is 7.9 inches.

Answer:Radius of the circle = 6 inchesCentral angle = 75 degrees.

Step-by-step explanation:

Answer:

[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]

Step-by-step explanation:

The question is not properly formatted.

Given

[tex]f(x) = x^3 - x^2 - 5x - 3[/tex]

[tex]g(x) =x + 3[/tex]

Required

[tex](\frac{f}{g})(x)[/tex]

This is calculated as:

[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](\frac{f}{g})(x) = \frac{x^3 - x^2 - 5x - 3}{x + 3}[/tex]

Factorize the numerator: using a calculator

[tex](\frac{f}{g})(x) = \frac{\left(x+1\right)^2\left(x-3\right)}{x + 3}[/tex]

Answer:

3, 11

The only common factor of Prime Numbers is 1

Answer:

No

Step Explanation:

I calculated it logically

Answer:

  28 toys

Step-by-step explanation:

Ben has 50 toys, of which 15 are new, 9 are favorites, and 2 are new and favorites. You want to know the number that are neither new nor favorite.

The number of new toys includes (new and favorite) and (new and not favorite). That is ...

  15 = 2 + new and not favorite

So ...

  new and not favorite = 15 -2 = 13

Likewise, the number of favorite toys includes (new and favorite) and (not new and favorite). That is ...

  9 = 2 + not new and favorite

  not new and favorite = 9 -2 = 7

The total of 50 toys includes ...

  total = (new and favorite) + (new and not favorite) + (not new and favorite) + (not new and not favorite)

  50 = 2 + 13 + 7 + (not new and not favorite)

Then the number of (not new and not favorite) is ...

  not new and not favorite = 50 -2 -13 -7 = 28

These are the toys that Ben gives away.

Ben gives away 28 toys.

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Answer:

18, 12

Step-by-step explanation:

Assuming this is follow-up from the previous question you asked? If not, I apologize for misunderstanding.

Dilation factor by 3 is bigger than 1 = Expansion

Originally 6, 4

6*3 = 18

4*3 = 12

Answer:

18,12

Step-by-step explanation:

W (1, -2), X (7,-2), Y (7,-6), and Z (1, -6).

To dilate the shape, multiply it's coordinates by the scale factor.

W'(3,-6), X'(21,-6), Y'(21,-18), Z(3, -18)

The distance formula: [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

plug W'(3,-6) and X'(21,-6) in to get the length

[tex]\sqrt{(3-21)^2+(-6-(-6))^2}=\sqrt{(-18)^2 +0^2}=\sqrt{324} =18[/tex]

plug X(21,-6) and Y(21,-18) to get the width

[tex]\sqrt{(7-7)^2+(-2-(-6))^2}=\sqrt{0^2 +4^2}=\sqrt{16} =4[/tex]

[tex]\sqrt{(21-21)^2+(-6-(-18))^2}=\sqrt{0^2 +12^2}=\sqrt{144} =12[/tex]

The given drug experiment is an example of observation.

There are three major types of statistical studies :

Given is that a doctor gives 10 patients Drug A and 10 patients Drug B and records the differences.

Giving 10 patients Drug A and 10 patients Drug B and then recording the differences is an example of observation.

Therefore, the given drug experiment is an example of observation.

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[tex]arc \ length = 2\pi r \frac{\theta}{360} = \\\\[/tex][tex]2 \pi *9 * \frac{135}{360} =21.205[/tex]

[tex]\frac{3\pi }{4} =\frac{3*180}{4}=135[/tex]

1.  you are asked to find how many weeks it would take Alex to work 51 hours.

2. Alex  works  [tex]3\frac{1}{7}[/tex] weeks.

3. It makes sense in fractional from.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Alex works 3 hours a day and 4 days a week.

Alex works in a week = ( 3×4) hour = 12 hour

Alex  works = 51 hours = 48 hours + 3 hours = (48/12) weeks + 1 day

= 3 weeks and 1 day.

= [tex]3\frac{1}{7}[/tex] weeks.

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Answer:

i think it would be d

Step-by-step explanation:

the median is just the middle of the numbers, it doesnt say which is the hardest question though

hope this helps.

The number of times 5×10³ greater than 15×10⁹ is 3×10⁶.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Given that, 15×10⁹ and 5×10³.

Number of times 5×10³ greater than 15×10⁹ is

Now, 15×10⁹/5×10³

= 3×10⁶

Therefore, 3×10⁶ times 5×10³ greater than 15×10⁹.

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Answer:

C. Paired t-interval for means

Step-by-step explanation:

The answer to this question is the paired t interval for means. The reason is because both of these events are independent. One of the event starts as the other event gets to it's completion. The population standard deviation is not also not known. This makes the paired t interval for means more suitable

Answer:

17/5

It is already simplified to lowest terms.

This number, as a mixed fraction, would look like this:

3 2/5.

Answer: x=3

Step-by-step explanation:

5x=7x-6

6+5x=7x

6=7x-5x

6=2x

solve for x which x=3

Answer:

x = 3

Step-by-step explanation:

Set the equations equal to each other:

5x = 7x - 6

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Division

Addition

Subtraction

~

Subtract 7x from both sides of the equation:

[tex]5x (-7x) = 7x (-7x) - 6\\5x -7x = -6\\-2x = -6[/tex]

Next, divide -2 from both sides of the equation:

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

*Remember that, when you divide two negative numbers, your answer will be positive:

[tex]x = \frac{-6}{-2} = 3[/tex]

3 is your answer for x.

x = 3.

~

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The distance from the top of the tree of height 30 tall to the end of the shadow is 50.

Distance is the length between two point.

To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.

Note: The tree and the shadow form a right angle.

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1

Hence, the distance from the top of the tree to the end of the shadow is 50.

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Answer:

a) Combination of 5 out of 30:

b) Combination of 2 males:

Combination of 3 females:

The number of ways with 2 males and 3 females:

c) Required probability is:

Answer:

it would be the graph with the maximum (opening down) in the first photo with the top on the left side of the y axis

Answer:

5 hours

Step-by-step explanation:

If shes going 59mph and the total trip is 295mph

then you would divid 295 by 59 and get 5

Answer:

A. Invalid

B. Valid

C. Valid.

Step-by-step explanation: A valid statement or argument is one in which the premise correlates with the conclusion.

It means that if all the premises are true then the conclusions from such premises must also be true. In the above statement, the first conclusion is invalid as it's conclusion does not correlates with its premise when considering the argument. Both conclusions B and C are valid as they correlates with their respective premises when considering the argument or statement made.

Answer:

Step-by-step explanation:

The LCM of 10,12,15 is 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 .

Answer:

60

Step-by-step explanation:

12a - 3b²

12(9) - 3(4)²

108 - 3(16)

108 - 48

60

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{12a - 3b^2}\\\mathsf{= 12(9) - 3(4)^2}\\\mathsf{= 12(9) - 3(4\times4)}\\\mathsf{= 12(9) - 3(16)}\\\mathsf{108 - 3(16)}\\\mathsf{= 108 - 48}\\\mathsf{= 60}\\\\\huge\text{Therefore, your answer should be: }\\\huge\boxed{\mathsf{60}}\huge\chdckmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.

If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.

Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.