Marco asked a group of friends to assist him with painting his room.The floor of his room is a rectangle 23.5 feet by 22.5 feet.He decided to paint the walls of his room light blue.The walls are 8.5 feet tall.What is the area he and his friends will need to paint?

Answer:

25%

Step-by-step explanation:

This is like a part over whole problem, where 24 blue pens is the part and 96 pens total is the whole.

24/96 = 0.25 * 100 = 25%

Answer:

Of the 96 pins, 25% of the pins were blue.

Step-by-step explanation:

We are given that Martina ordered 96 pins in total. We are also given that she ordered 24 blue pins.

With this, we can determine how many of the pins were not blue pins by subtracting the amount of blue pins from the number of total pins.

\(96 \ \text{total pins} - 24 \ \text{blue pins} = 72 \ \text{orange pins}\)

Now, we can divide the number of blue pins by the number of total pins to determine the fraction of blue pins to total pins.

\(\displaystyle \frac{24}{96} = \frac{12}{48} = \frac{6}{24} = \frac{3}{12} = \frac{1}{4}\)

Then, we can convert our fraction to a decimal.

\(\displaystyle \frac{1}{4} = 0.25\)

And finally, we can convert our decimal to a percentage by multiplying the determined decimal by 100.

\(0.25\times100 = 25\%\)

Therefore, of the 96 pins that Martina ordered, 25% of them were blue.

The number of heavy equipment operators employed is 26 while number of laborers employed is 6

Let x be the number of heavy equipment operators employed

Thus, If thirty-two people were hired, then we can say that;

32 - x represents the number of laborers employed

Thus, the equation to solve for x would be;

136x + 80(32 - x) = 3960

136x + 2560 - 80x = 3960

216x + 2560 = 3960

216x = 3960 - 2560

216x = 1400

x = 1400/216

x ≅ 6

Thus;

32 - x = 32 - 6 = 26

Thus, we conclude that number of heavy equipment operators employed is 26 while number of laborers employed = 6

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The distance traveled by a particle with velocity v(t) in the interval [3,13] is given by the following integral:

However, we can't calculate this integral since we don't have the equation of v(t). What we do have is a table with the value of v for several t's. We can use the values in this table to approximate the integral I wrote above with a trapezoidal sum.

For the function v(t) we have:

Where the t's with subindices are the t values given by the table:

And the Δt's are the lengths of the intervals defined by two consecutive t's. Let's find each Δt:

Now I'm going to write the full expression of the trapezoidal sum (expanding the sum):

Now we use the corresponding v(t) values from the table and we obtain:

Then the answer is the third option, 115.50.

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)

\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)

The dimensions that would maximize the area enclosed by the fence is 30m × 60m.

where

l = length

w = width

Therefore,

The corral uses the side of a barn as one of its sides, so the fencing is required on three sides of the rectangular region. Therefore,

perimeter = L + 2w

L + 2w = 120

L = 120 - 2w

area = Lw

area = (120 - 2w)w

area = 120w - 2w²

area = -2w² + 120w

We have a quadratic equation and it is parabolic.  The leading coefficient is negative. Therefore, the parabola opens downward and the vertex is the maximum point.

The area is maximized at the vertex. Therefore,

To find the vertex, we need to have our quadratic equation in general form,

ax² + bx + c = 0

so a = -2, b = 120

w = -b / 2a

w = - 120 / 2 × -2

w = -120 / -4

w = 30

Therefore,

area = -2(30)² + 120(30)

area = 1800m²

Therefore, the maximum area we can enclose is 1800 m², the width is 30m, then the length will be 60 m because 60 × 30 = 1800 m².

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Answer:

2b

Step-by-step explanation:

Answer:

number 2 is 20 percent so j

Step-by-step explanation:

Answer:

90.24 in²

Step-by-step explanation:

Area of the pizza :

⇒ Area (rectangle) + Area (semicircle)

⇒ length × width + π × (radius)²

⇒ 8 x 5 + 3.14 x 4²

⇒ 40 + 3.14 × 16

⇒ 40 + 50.24

⇒ 90.24 in²

The area of a 2D form is the amount of space within its perimeter. The area of the pizza is 65.1327 in².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the pizza = Area of semi-circle + Area of Rectangle

                                   = (π/2)r² + (d×h)

                                   = [(π/2)×4²] + (8×5)

                                   = 25.1327 in² + 40 in²

                                   = 65.1327 in²

Hence, the area of the pizza is 65.1327 in².

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Answer:

13x^2 - 6x -11

Step-by-step explanation:

Answer:

Answer:

10x-3=7x+45 corresponding angle

10x-7x=45+3

3x=48

x=48/3=16

value of x is 16.

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

Using thie model ,The answer is D. 27.

To calculate 9÷1/3 using the model below, we can imagine dividing the green rectangle into thirds vertically. Each third would contain 3 cells.

Then, we can see that there are a total of 9 cells in the rectangle. Since we are dividing by 1/3, we need to find out how many sets of 1/3 are in 9.

We can see that there are 3 sets of 1/3 in each row (since each row contains 3 cells, which are thirds). So, in total, there are 3 rows of 3 sets of 1/3, which gives us:

9÷1/3 = 3 rows x 3 sets of 1/3 = 9 sets of 1/3 = 27

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Answer:

y=9x+2

Step-by-step explanation:

The standard form for a linear equation is y=mx+b. m=9 since it is slope and b=2 which is the y intercept. So the equation would be y=9x+2.

Mrs. Smith will need 64m² of floor covering for her master bedroom.

The length L of the bedroom is 11 yards,

The breadth B of the bedroom is 7 yards.

The floor covering is available only in square meters.

As we know,

One yard = 0.9144 meters.

the length of the bedroom in meter is,

Length L = 0.091144 x 11

Length L = 10.02 meters.

the breadth of the bedroom in meters is,

Breadth B = 0.91144 x 7

Breadth = 6.38 meters.

the Area of Rectangular master bedroom in Meter square is,

Area = Length x Breadth

Area of the bedroom = 10.02 x 6.38

Area of the bedroom = 63.92 m²

Area of floor covering required = Area of the master bedroom.

Area of the floor covering required = 63.92 m².

Rounding off to nearest hundredth = 64m²

Mrs. Smith will need 64m² of floor covering.

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The general solution is y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3C)^(1/3), the particular solution is y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3(55.458333))^(1/3), and the interval of validity is (-∞, ∞).

To separate the given differential equation and integrate to find the general solution, we need to follow the following steps:

Step 1: Separate the variables on each side of the equation: y^2 e^-7X y'=x => y^2 dy = x e^7X dx

Step 2: Integrate both sides of the equation: ∫y^2 dy = ∫x e^7X dx => (y^3)/3 = (e^7X)/49 - (x e^7X)/7 + C

Step 3: Solve for y to find the general solution: y^3 = 3((e^7X)/49 - (x e^7X)/7) + 3C => y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3C)^(1/3)

The general solution is y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3C)^(1/3)

To find the particular solution that satisfies the initial condition y(0) = 5.5, we need to plug in the initial condition into the general solution and solve for C:

5.5 = (3((e^(7*0))/49 - (0 e^(7*0))/7) + 3C)^(1/3) => 166.375 = 3C => C = 55.458333

Now, we can plug in the value of C into the general solution to find the particular solution:

y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3(55.458333))^(1/3)

The particular solution is y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3(55.458333))^(1/3)

The interval of validity for this solution is the entire real number line, since there are no restrictions on the values of x or y. Therefore, the interval of validity is (-∞, ∞).

In conclusion, the general solution is y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3C)^(1/3), the particular solution is y(x) = (3((e^7X)/49 - (x e^7X)/7) + 3(55.458333))^(1/3), and the interval of validity is (-∞, ∞).

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Answer:

The first choice.

Step-by-step explanation:

6 * 10^8 /  1.5 * 10^-4

= (6/1.5)  * (10^(8 - (-4))

= 4 * 10^12.

Answer:

4 x 1012

Step-by-step explanation:

The inverse of the given matrix would be C. C ⁻¹ [-4.5, -3.5]

[ - 4 , - 3 ]

The formula for finding the inverse of the matrix is;

= ( 1 / determinant ) x [ d , - b ]

[ - c , a ]

The inverse is therefore:

= 1 / 2 x [ 9 , 7 ]

=  [- 4. 5 , - 3 . 5 ]

= [ - 4 , - 3 ]

So, the inverse of the matrix C is:

[ - 4. 5 , -3. 5 ]

[ - 4 , - 3 ]

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Answer:

4

Step-by-step explanation:

i did math

Answer: 4  

Step-by-step explanation:

The Greatest common factor is the largest factor that both numbers share, so find their factors,

Factors of 20:  1,2,4,5,10 and 20

Factors of 36:  1,2,3,4,6,9,12,18, and 30

The largest factor that both numbers share  is 4

Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

Answer:

The perimeter is 57.2 cm and the area is 198.73 cm^2

Step-by-step explanation:

Step 1:  Determine the perimeter

\(Perimeter = 2(l + w)\)

\(Perimeter = 2(16.7\ cm + 11.9\ cm)\)

\(Perimeter = 2(28.6\ cm)\)

\(Perimeter = 57.2\ cm\)

Step 2:  Determine the area

\(Area = l * w\)

\(Area = 16.7\ cm * 11.9\ cm\)

\(Area = 198.73\ cm^2\)

Answer: The perimeter is 57.2 cm and the area is 198.73 cm^2

Answer:

if you are trying to find x:

c) 1/12=x     d)1/30=x

Step-by-step explanation:

2/3x=8

2=24x

1/12=x

3/5x-10=8

3/5x=18

3=90x

1/30=x

Answer:

4

Step-by-step explanation:

Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

Answer:

R = 21

Step-by-step explanation:

525 ÷ 28 = 18 R 21

28 × 18 = 504

525 - 504 = 21

Therefore, the remainder is 21.

Hope this helps! :)

The remainder of 525 divided by 28 is 21

First step

Division

525 ÷ 28

= 18

Second step multiply 28 by 18

28 × 18

= 504

Now let determine remainder of 525 divided by 28

Remainder=525 - 504

Remainder= 21

Inconclusion remainder of 525 divided by 28 is 21

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Answer:

x= -16

Step-by-step explanation:

add 11 to each side.

-2=x/8

multiply both sides by 8

-16=x

Answer:

y=7x+8

then interchange x and y

x=7y+8

then

x-8=7y

y=X-8/7

Answer:

Step-by-step explanation:

1. (4x5) is 20

2. (4x 2) is 8

3. 20 plus 8 is 28

4. 28= 4x (5+n)

5. isolate n by dividing 4 on both sides= 28/4= 4+n

6. subtract 4 on both sides to get 7-4=n

7. n=3

It should be noted that sbsolute risk is the probability of an event.

It should be noted that absolute risk is used for the number of events which occurred in a group which is divided by the number of people in that group.

The response variable is the focus of a question in the experiment and an explanatory variable is one which explains changes in that variable.

The types of bar graph include:

The steps involved for the pie chart include:

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Answer:

between 14 and 15

Step-by-step explanation:

convert fractions using 42 as the LCD, then add:

59/7 = 354/42

37/6 = 259/42

354/42 + 259/2 = 613/42 = 14.6

14 < 14.6 < 15

or,

convert fractions to decimals, then add:

59/7 = 8.4

37/6 = 6.2

8.4 + 6.2 = 14.6