Use the triangle shown to find the ratios.

cos(A) =
tan(C) =

The area of the room = (40 x 24) - (20 x 12)

Area = 960 - 240 = 720 square feet

Divide square feet by width of a strip:

720 / 12 = 60 linear feet.

The answer is D.

Answer : The correct option is, (D) 60

Step-by-step explanation :

First we have to calculate the area of room.

Area of room = Area of big rectangle + Area of small rectangle

Area of rectangle = Length × Width

Area of room = (40 × 12) + (20 × 12)

Area of room = 720 square feet

Now we have to calculate the number of linear feet will he need to buy.

Number of linear feet = [tex]\frac{\text{Area of room}}{\text{Width of carpet strips}}[/tex]

Number of linear feet = [tex]\frac{720}{12}=60[/tex]

Thus, the number of linear feet will he need to buy is, 60

Answer:

Step-by-step explanation:

[tex]-38=7v+17-12v\qquad\text{subtract 17 from both sides}\\\\-38-17=7v+17-17-12v\qquad\text{combine like terms}\\\\-55=-5v\qquad\text{divide both sides by (-5)}\\\\\dfrac{-55}{-5}=\dfrac{-5v}{-5}\\\\11=v\to v=11[/tex]

Answer:

Step-by-step explanation:

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Answer:

GCF(15,20) = 5

Step-by-step explanation:

Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:

15 = 31 × 51

Prime Factorization of 20

Prime factors of 20 are 2, 5. Prime factorization of 20 in exponential form is:

20 = 22 × 51

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5

Factors of 20

List of positive integer factors of 20 that divides 15 without a remainder.

1, 2, 4, 5, 10

Greatest Common Factor

We found the factors and prime factorization of 15 and 20. The biggest common factor number is the GCF number.

So the greatest common factor 15 and 20 is 5.

Answer:

16

Step-by-step explanation:

because eight is 50% of 16

Answer: She will be 16

Step-by-step explanation:

Answer:

A. 1/36 B. 1

Step-by-step explanation:

A. if (6^2)x=1; 6^2=36

36x=1

x=1/36

B. If (6^0)x=1; 6^0=1

(1)x=1

x=1

Answer:

173,482-5.5=173,476.5

Answer:

$9,541.51

Step-by-step explanation:

The classification of the numbers into rational and irrational are:

1. Pi is irrational

2. 7 squared is irrational

3. 7.1234... is irrational

1) π is a mathematical expression whose approximate value is 3.14159365…

The given value of π is expressed in decimal which is non-terminating and non-repeating. As the value is non-terminating it shows the nature of irrational numbers. Hence, π is not a rational number

2) 7 squared is not a perfect square and as such it will have non-terminating and non-repeating decimal and so it is irrational.

3) 7.1234... is an irrational number because it is non-terminating and non-repeating decimal.

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Answer:

B. 2 m

Step-by-step explanation:

cm are centimeters and mm means millimeters and these a both smaller than an inch, and km kilometers is a distance like miles. Whilst m stands for meters.

Answer:

Step-by-step explanation:

(−4.46)(11)=−49.06

Final answer:

To create a 35% saline solution by mixing a 50% and a 30% solution, the nurse needs to use 6000cc of the 30% solution.

Explanation:

The question asks how much of a 30% saline solution a nurse needs to mix with 60cc of a 50% saline solution to achieve a final solution concentration of 35%. To solve this problem, let's denote the volume of the 30% solution needed as x cc. Using the concept of weighted averages for concentrations, we can set up the following equation:

(60cc × 50%) + (x cc × 30%) = (60cc + x cc) × 35%

Solving this equation, we get:

3000 + 0.3x = 0.35(60 + x)

3000 + 0.3x = 21 + 0.35x

Subtracting 0.3x from both sides:

3000 = 21 + 0.05x

Subtracting 21 from both sides and dividing by 0.05:

x = 6000 cc

Therefore, the nurse should use 6000cc of the 30% saline solution to achieve the desired concentration.

Check the picture below.

The measure of m∠EBC if m∠EBD = 36° and m∠DBC = 108° is 144degrees

The point where two lines intersect is known as the angle.

From the diagram shown:

m∠EBC = m∠EBD + m∠DBC

Given the following:

m∠EBD = 36degrees

m∠DBC = 108degrees

Substitute the given values into the expression as shown:

m∠EBC = 36 + 108

m∠EBC = 144degrees

Hence the measure of m∠EBC is 144degrees

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Paulo's time in standard notation is 15,600 seconds. Miguel ran the marathon in a shorter time of 15,360 seconds. For the given equations, A) and B) each have one solution (x=3 and x=10, respectively), while C) has an infinite number of solutions.

To convert Paulo's time from scientific to standard notation, we multiply 1.56 by 10 to the power of 4. This equals 15,600 seconds. Next, we need to convert Miguel's time to seconds to directly compare the two durations. Miguel ran for 4 hours and 16 minutes, which is equal to (4 × 3600) + (16 × 60) = 14,400 + 960 = 15,360 seconds. Therefore, Miguel ran the race in a shorter amount of time by 240 seconds.

For question 2, we solve the following equations:

For equation A) 2x + 4(x - 1) = 2 + 4x, after simplifying we get 2x + 4x - 4 = 2 + 4x. The 4x terms cancel out and we are left with 2x - 4 = 2. Solving for x gives x = 3. This equation has one solution.

For equation B) 25 - x = 15 - (3x + 10), simplifying gives 25 - x = 5 - 3x. Solving for x yields x = 10, so this equation also has one solution.

For equation C) 4x = 2x + 2x + 5(x - x), simplifying results in 4x = 4x, which is true for all values of x. Therefore, this equation has an infinite number of solutions.

As question 3 involves an image that we cannot see here, this part of the student's question has been left unanswered.

Answer:

Step-by-step explanation:

The mean (or average) of a set of numbers can be found with the following formula:

[tex]Mean = \frac{A_{1} + A_{2} + ... + A_{N}}{N}[/tex]

For this problem, we have five numbers, so we add them together and divide by 5:

[tex]Mean = \frac{92 + 85 + 78 + 97 + 88}{5}[/tex]

[tex]Mean = \frac{440}{5}[/tex]

[tex]Mean = 88[/tex]

Answer:

88%

Step-by-step explanation:

Emma took tests of her 5 chapters throughout the year.

She received  the score on the five tests

92%, 85%, 78%, 97% and 88%

We have to calculate the average (mean) of her final grade.

average =  [tex]\frac{\text{addition of all grades}}{\text{total number of tests}}[/tex]

=  [tex]\frac{92+85+78+97+88}{5}[/tex]

=  [tex]\frac{440}{5}[/tex]

= 88%

Her final grade would be 88%.

Answer:

x = 3.65

Step-by-step explanation:

7.4x + 5 = 32

-5              -5

7.4x = 27

-----    -----

7.4     7.4

x = 3.64864865

This rounds to 3.65

x = 3.65

Answer:

B. No solutions.

Step-by-step explanation:

Let's try solving it:

3(x + 8) = 3x + 4

3x + 8 = 3x + 4.

There are no solutions  because if we simplify we get an absurd result. Subtract 3x from both sides of the equation:

3x - 3x + 8 = 3x - 3x + 4

8 = 4.

There are no solutions for x in this equation.

To solve this equation, we need to combine like terms and isolate the variable. Here are the steps:

Since 23 does not equal 4, these two sides are not equal. Therefore, there are no solutions for x in this equation.

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Answer: 17

Step-by-step explanation:

Gabby's savings over 'b' weeks can be written as an inequality 50 + 20b > 400. Simplifying this, we find that Gabby has to save up for at least 18 weeks to save more than $400.

Gabby's savings can be represented as 50 + 20b, with 'b' being the number of weeks. For her to save more than $400, we can write this inequality 50 + 20b > 400. Subtract 50 from both sides to simplify the inequality and we get 20b > 350. To find the least number of weeks, divide both sides by 20 to solve for b and we get b > 17.5. However, since 'b' must be a whole number (because you can't have half a week), the least number of weeks Gabby must save is 18 weeks.

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Answer:

Step-by-step explanation:

11. I can't see the full problem statement, so I'm unable to answer the question.

12. Answer below:

"one half" = [tex]\frac{1}{2}[/tex]

"negative five eighths" = [tex]\frac{-5}{8}[/tex]

To evaluate the expression, you multiply the two numbers together:

[tex]\frac{1}{2} * \frac{-5}{8} = \frac{1 * -5}{2 * 8} = \frac{-5}{16}[/tex]

13. Answer below:

"one third" = [tex]\frac{1}{3}[/tex]

"eleven sixteenths" = [tex]\frac{11}{16}[/tex]

To evaluate the expression, you multiply the two numbers together

[tex]\frac{1}{3} * \frac{11}{16} = \frac{1 * 11}{3 * 16} = \frac{11}{48}[/tex]

Answer:

x^(1/12).

Step-by-step explanation:

By the laws of indices:

(x ^ 1/2)^1/6)

= x ^(1/2*1/6)

= x^(1/12).

Answer:

if you're asking what 21 divided by 40 is then it's 0.525

Step-by-step explanation:

Hey!

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

Find the zero term:

Plug in 0 for n.

a = 8 + 3(0 - 1)

a = 8 + 3(-1)

a = 8 + (-3)

a = 5

Answer: 5

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

Find the first term:

Plug in 1 for n.

a = 8 + 3(1 - 1)

a = 8 + 3(0)

a = 8 + 0

a = 8

Answer: 8

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

Find the 40th term:

Plug in 40 for n.

a = 8 + 3(40 - 1)

a = 8 + 3(39)

a = 8 + 117

a = 125

Answer: 125

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

Hope This Helped! Good Luck!

Answer:

The answer is 2/3 okay? Pls thx me!

Answer:

3t-2

Step-by-step explanation:

Answer:

0.55 or 55/100 or 11/20

Step-by-step explanation:

Hey there!

3/10 + 1/4

≈ 6/20 + 5/20

= 6 + 5 / 20 - 0

= 11 / 20

Thus, your answer is: 11/20

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Dave should stop at Springfield.

Step-by-step explanation:

As shown, Gilmore is 26 miles away.

And Dave is driving to Gilmore but he wants to stop for lunch when he is about halfway there.

That means he wants to stop around [tex]\frac{26}{2}=13[/tex] miles.

And Springfield is 15 miles away that is nearest to 13 miles.

Hence, Dave should stop at Springfield.

Answer:

18,21,36

Step-by-step explanation:

Final answer:

4.17 can be written as 4 17/100.

Explanation:

The number 4.17 can be written as a whole number with a fraction by separating it into the whole number part and the fractional part.

Thus, 4.17 can be written as 4 17/100.

Answer:

1  5/6

Step-by-step explanation:

ab = (-2 3/4) * (-4/6)

     = ( -11/4) * ( -4/6)

     = (11 * 4) / (4 * 6 )

      = 11/6

       = 1  5/6

Answer:

[tex](34)[/tex]

Step-by-step explanation:

We are looking for what number times .50 makes the equation true.

So, just do backwards equation:

[tex]52 - 35[/tex]

[tex]==> 17[/tex]

Thus, meaning that what multiplied by 0.50 is equal to 17?

[tex]0.50 * 34[tex]

[tex]==> 17[tex]

Put any Variable in between the parentheses, for example x.

Step-by-step explanation:

1. Move the Constant 35 to the other side of the problem, and flip it's sign.

0.5(×)=52-35

2. Subtract the numbers

0.5×=17

3. Divide both sides of the equation by 0.5

×=34

Answer:

Step-by-step explanation:

We know:

1min = 60s → 3min = (3)(60s) = 180s

40s : 3min = 40s : 180s = (40/20) : (180/20) = 2 : 9

$1 = ¢100 → $3 = (3)(¢100) = ¢300

$3 : ¢65 = ¢300 : ¢65 = (300/5) : (65/5) = 60 : 13