(It's a fraction). 5/2 + 5/7

The area of the rectangle is 2000 square inches.

Given that the length of a rectangle is five times its width, if the perimeter of the rectangle is 120 inch, the following calculation must be performed to find its area:

Therefore, the area of the rectangle is 2000 square inches.

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The width of the rectangle is 10 inches and the length is 50 inches. The area of the rectangle is 500 square inches.

Let's denote the width of the rectangle as w. Since the length of the rectangle is five times its width, we can write the length as 5w. The formula for the perimeter of a rectangle is P = 2(l + w), so we can set up the equation 120 = 2(5w + w). Solving this equation, we find that the width is 10 inches and the length is 50 inches.

To find the area of the rectangle, we use the formula A = l * w. Plugging in the values for length and width, we get A = 50 * 10 = 500 square inches. Therefore, the area of the rectangle is 500 square inches.

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Answer:

[tex]\large\boxed{4\sqrt3}[/tex]

Step-by-step explanation:

[tex]\text{A geometric mean of}\ a\ \text{and}\ b:\\\\\sqrt{ab}\\\\\text{We have}\ a=4,\ b=12.\\\\\text{Substitute:}\\\\\sqrt{4\cdot12}=\sqrt{48}=\sqrt{16\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{16}\cdot\sqrt3=4\sqrt3[/tex]

Answer:

6.2% of last month's income was spent on office expenses

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Office's income last month = $ 315,600

Expenses last month = $ 19,567.20

2. What percent of last month's income was spent on office expenses?

To calculate this percent, we use this fraction:

Expenses last month/Office's income last month

Replacing with the real values:

19,567.20/315,600 = 6.2%

6.2% of last month's income was spent on office expenses

Final answer:

Tom's real estate office spent 6.2% of its income on office expenses last month. This was calculated by dividing the expenses by the income and then multiplying by 100.

Explanation:

To determine what percent of last month's income was spent on office expenses for Tom's real estate office, you need to use the formula for calculating the percentage of expenses relative to income. The formula is:

Percentage of Expenses = (Expenses ÷ Income) × 100

Now, we were given that the office's income last month was $315,600 and the expenses were $19,567.20. Substituting these numbers into our formula gives us:

Percentage of Expenses = ($19,567.20 ÷ $315,600) × 100

Percentage of Expenses = (0.062 × 100)

Percentage of Expenses = 6.2%

Therefore, 6.2% of last month's income was spent on office expenses.

Answer: a= -4

Step-by-step explanation:

Final answer:

To solve the equation 4a+5=2+3.25a, isolate the variable 'a' on one side of the equation. The solution is a = -4.

Explanation:

To solve the equation 4a+5=2+3.25a, we need to isolate the variable 'a' on one side of the equation.

Step 1: Subtract 3.25a from both sides of the equation:

4a - 3.25a + 5 = 2

0.75a + 5 = 2

Step 2: Subtract 5 from both sides of the equation:

0.75a = 2 - 5

0.75a = -3

Step 3: Divide both sides by 0.75 to solve for 'a':

a = -3/0.75

a = -4

Therefore, the solution for the equation 4a+5=2+3.25a is a = -4.

Answer: 48.07

Step-by-step explanation:

48.073 Rounded to the Nearest Hundredth

To round 48.073 to the nearest hundredth consider the thousandths' value of 48.073, which is 3 and less than 5. Therefore, the hundredths' value of 48.073 remains 7.

Answer:

2400m³

Step-by-step explanation:

50 * 30 * 1.6 =

1500 * 1.6 = 2400m³

The speed in feet per second is 247.5

The parachutist will fall 4950 feet during 20 seconds.

Step-by-step explanation:

Given,

Speed during free fall = 75 meters per second

It is given that,

1 meter = 3.3 feet

75 meter = 75*3.3 = 247.5 feet

Therefore;

Speed during free fall in feet = 247.5 feet per second

Now,

1 second = 247.5 feet

20 seconds = 247.5*20 = 4950 feet

Fall during 20 seconds = 4950 feet

The parachutist will fall 4950 feet during 20 seconds.

Keywords: multiplication

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The parachutist's speed in freefall, converted to feet per second, is 247.5 feet per second. In 20 seconds of free-fall, the parachutist would fall a total of 4950 feet.

The parachutist's speed in free-fall is given as 75 meters per second. We know that 1 meter is equivalent to approximately 3.3 feet. So, to convert the speed from meters per second to feet per second, we multiply the speed in meters per second by 3.3. This gives us a speed of 75 * 3.3 = 247.5 feet per second.

Then, to find out how many feet the parachutist will fall during 20 seconds of free fall, we multiply the speed in feet per second by the time in seconds, which results in 247.5 * 20 = 4950 feet.

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Answer:

25

Step-by-step explanation:

13x7=91

268-91=177

177÷7=25

The bakery sells approximately 25 cookies per day.

To find how many cookies are sold per day, we first need to determine the total number of pies sold in 7 days.

Total sales (pies + cookies) for 7 days is given as 268.

Thus, the bakery sells approximately 25 cookies per day.

Answer:

3+8g

Step-by-step explanation:

27/9+8g=3+8g

Answer:

392b²

Step-by-step explanation:

56b×77b÷11

56b×7b

392b²

Answer:

[tex]A = w^2 + 7w[/tex]   is the rule for the area of a rectangle.

A = 120 sq ft, when it’s width is 8 ft.

Step-by-step explanation:

Here, let us assume the width of the rectangle =  w

So, the length here = Width +  7 ft = (w +  7) ft

Now, AREA of a RECTANGLE = Length x Width

Substituting here the values of length and width, we get:

A = (w) x (w +  7) [tex]= w^2 + 7 w[/tex]

[tex]\implies A = w^2 + 7w[/tex]

The above function is the rule for the area of a rectangle.

Given: w = 8  ft

To find the area: put w  = 8 in [tex]A = w^2 + 7w[/tex]

We get: A  = 8²  +  7(8)  

                 = 64 +  56  = 120

or, A  = 120 sq ft.

Hence, area = 120 sq ft, when it’s width is 8 ft.

Answer:

Step-by-step explanation:

[tex]i^{20}+1=i^{2*10}+1\\\\(i^{2})^{10}+1=(-1)^{10}+1\\\\=1+1=2[/tex]

Answer:

$31.20

Step-by-step explanation:

Angela will get an amount of $31.2 as the interest at the end of 1 year.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that Angela puts $520 in an account that earns 6% per year.

Principal or initial amount = $520

Rate of interest = 6% = 6 / 100 = 0.06

We have to calculate the amount of interest.

Interest amount = $520 × 0.06

                           = $31.2

Hence the amount of interest that Angela get at the end of the year is $31.2.

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Answer:

48...

Step-by-step explanation:

12(4) equals 48oz

48oz= 3lb

Answer:

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 3, 3)  

point B( x₂ , y₂) ≡ (5 , -1)  

point C( x₃ , y₃) ≡ (-2 , 1)

To Find:

Centroid, G (x,y) = ? (say)

Solution:

Centroid:

Centroid is a point where all the three medians of the triangle intersect.

It is denoted as G and the coordinates are give by

[tex]G(x,y)=(\dfrac{x_{1}+x_{2}+x_{3}}{3},\dfrac{y_{1}+y_{2}+y_{3}}{3})[/tex]

Substituting the values we get

[tex]G(x,y)=(\dfrac{3+5+-2}{3},\dfrac{3+-1+1}{3})[/tex]

[tex]G(x,y)=(\dfrac{6}{3},\dfrac{3}{3})=(2,1)[/tex]

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]

Answer:

B.

Step-by-step explanation:

1000 meters in a kilometer and 60 minutes in a hour. 1000/60= 16.6666

(rounds to 20)

Final answer:

Charles' running speed of 12 kilometers per hour is equivalent to 200 meters per minute when converted, which corresponds to option D.

Explanation:

Charles runs at a rate of 12 kilometers per hour, and the question asks us to convert this speed to meters per minute. First, we need to convert kilometers to meters. One kilometer is equivalent to 1,000 meters.

So, Charles' speed in meters per hour is:

12 km/hr × 1,000 m/km = 12,000 m/hr

To convert this speed from meters per hour to meters per minute, we divide by 60 minutes, since there are 60 minutes in one hour:

12,000 m/hr ÷ 60 min/hr = 200 m/min

Therefore, Charles' speed is 200 meters per minute, which corresponds to option D.

Answer:

i think that it's c

Step-by-step explanation:

Answer:

Domain: (-oo, oo)

Range: (-4,oo)

Horizontal asymptote: y=-4

Answer:

The domain is all Real numbers.

The range is all real values > -4.

Step-by-step explanation:

The asymptote is y = -4.

The number of bacteria in the colony after n hours is 2,500 × (1 + 0.11)ⁿ.

Exponential growth N = N0 × (1 + r)ᵃ

Where N = final population size

N0 = initial population size

r = growth rate

a = time in hours

After n hours the colony's size = 2,500 × (1 + 0.11)ⁿ.

Question:

Let p: x = 4 Let q: y = −2 Which represents "If x = 4, then y = −2”? p ∨ q p ∧ q p → q p ↔ q

Answer:

Option c: p → q

Explanation:

Option a: p ∨ q

p ∨ q means that either p is true or q is true or both are true.

Hence, Option a is not the correct answer.

Option b: p ∧ q

p ∧ q means that both p and q are true.

Hence, Option b is not the correct answer.

Option c: p → q

p → q means that if p is true, then q is also true.

Hence, Option c is the correct answer.

Option d: p ↔ q

p ↔ q means that if p is true, then q is true. If q is true, then p is true.

Hence, Option d is not the correct answer.

Thus, p → q is the correct option.

Answer:

x=8/7

Step-by-step explanation:

2/3=x/4+x/3

3x/12+4x/12=8/12

7x/12=8/12

x=(8/12)/(7/12)

x=(8/12)(12/7)

x=8/7

Answer:

1. The answer is B.

2.The answer is A.

Answer:

A

Step-by-step explanation:

Blueberry = 4 1/2 = 9/2

Raspberry = 1 4/6 = 10/6 = 5/3

Strawberry = 3 2/5 = 17/5

Total berries = sum total of all the berries = 9/2 + 5/3 + 17/5

The LCM is 30

Total berrie={9(15) + 5(10) + 17(6)}/30

= (135 + 50 + 102)/30

= 287/30

= 9 17/30

Answer: 785.5

Step-by-step explanation:

Final answer:

To solve 2 divided by 1571, recognize it as a fraction 2/1571, which cannot be simplified. Perform long division, adding zeros as necessary, to find its decimal representation, which will be very small.

Explanation:

To solve 2 divided by 1571 step by step without a calculator, you can follow these steps:

Understand that this division represents a fraction, 2/1571.

Recognize that this fraction cannot be simplified further since 2 and 1571 have no common factors other than 1.

To find the decimal form, you can perform long division. However, since 2 is much smaller than 1571, the decimal will start with 0. As 2 cannot be divided by 1571, in the first step of long division, you would put a 0 to the right of the decimal point in your answer.

Next, you would need to add a 0 to the right of 2 (making it 20), since 1571 still cannot go into 2. Then, determine how many times 1571 can go into 20, which will still result in 0, and so on, adding zeros and comparing until you reach a desired level of precision.

This process will yield a very small decimal, indicating that 2/1571 is a fraction much less than 1.

Answer:

Option D: The area will be multiplied by 16.

Step-by-step explanation:

Given that the area of the figure is 13 sq. in.

Let is say the figure is of dimensions: a & b.

Therefore, a.b = 13 sq. in

When each of the dimension is multiplied by 4, the dimensions would become 4a and 4b.

Therefore, the area would be: 4a . 4b = 16 a . b = 16(13) sq. in.

Hence, the area is multiplied by 16.

Answer:

y= -1 , -3 , -5

Step-by-step explanation:

2x-3y=9

2x-9=3y

2x-9/3=y

when x=0

y= -9/3

y= -3

when x= 3

y = 2(3)-9/3

  = 6-9/3

  = -3/3

y = -1

when x= -3

y = 2(-3)-9/3

y= -6-9/3

y= -15/3

y= -5

To solve the equation 2x-3y=9 for y in terms of x, firstly move the '2x' on right side of the equation to get -3y = -2x + 9. Multiply each term by -1 to get 3y = 2x - 9. And then divide each term by 3 to get y = (2/3)x - 3.

In order to solve the equation 2x-3y=9 for y in terms of x, we first isolate y. The first step would be to move '2x' part to the right side of the equation. It becomes like this: -3y = -2x + 9 or simply, 3y = 2x - 9 where we multiplied every part of the equation by -1. Now, the next step is to get rid of '3' that is multiplying 'y'. For this, you divide entire equation by '3'. Hence, y = (2/3)x - 3. So, the equation for y in terms of x is y = (2/3)x - 3.

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Answer:

In Grade 8, 17% of students liked running

Step-by-step explanation:

Although this table is incomplete, there are still enough information to answer.

First, we need to be aware that the data here is written in decimal numbers, which is another way to write percentages.

In other words, 100% equals to 1, which is to say that if we multiply decimal number with 100 we'll get the percentage:

0.39 = 39%

0.04 = 4%

Another important thing to establish is that the value of decimal number DOES NOT mean the number of people, it only suggests the ratio:

0.26 does not mean 26 people etc.

Knowing this, from this incomplete table, we see that 0.17 students from grade 8 liked running. And now we know that 0.17 equals to 17%, which makes B the correct answer.

Answer:

B. In Grade 8, 17% of students liked running

Step-by-step explanation:

Answer:

The number of adult ticket sold is [tex]12[/tex]

The number of child ticket sold is [tex]38[/tex]

Step-by-step explanation:

Given cost of adult tickets are $[tex]8[/tex], and cost of child tickets are $[tex]4[/tex]

Let the number of adult ticket sold is [tex]x[/tex]

Also, the number of child ticket sold is  [tex]y[/tex]

We can write two equation from given information.

[tex]x+y=50\ Equation\ (1)\\8x+4y=248\ Equation(2)[/tex]

Now, plug [tex]x=50-y[/tex] in [tex]Equation(2)[/tex] we get,

[tex]8(50-y)+4y=248\\400-8y+4y=248\\-4y+400=248\\-4y=248-400\\-4y=-152\\y=\frac{-152}{-4}\\y=38[/tex]

Now, from [tex]Equation(1)[/tex]

[tex]x+y=50\\x+38=50\\x=50-38\\x=12[/tex]

So, The number of adult ticket sold is [tex]12[/tex]. And the number of child ticket sold is [tex]38[/tex]

Answer:

2) -1

Step-by-step explanation:

it is easy

 we have to first open the brackets, as it is ' - '  we have to change the sign to opposite of that of the number in the bracket and then solve it.

so the number 2 is having negative sign, we make it positive. this rule is applied only when there is a negative sign and a bracket is there.

-3-(-2)

-3+2

=-1

Answer:

it has only one solution

Step-by-step explanation:

Answer:

-1000

Step-by-step explanation:

(5r)^3 for r = -2

(5 x +2)^3 =

(-10)^3 =

-1000