If a train is accelerating at 30m/s after it takes off from the train station and travels for 60 seconds, what was its final velocity?

Answer:

The side length of the blocks is 5 inches

the total surface area of the 27 blocks = 27 x 150 = 4050 square inches

This is 3 times the surface area of the box.

Explanation:

From the information given,

the cube shaped box with side length of 15 inches contains 27 identical cube-shaped blocks. Recall, the length of each side of a cube is equal. We would calculate the volume of the cube shaped box. The formula for calculating the volume of a cube is

Volume = s^3

Volume of cube shaped box = 15^3 = 3375

Thus,

Volume of 27 identical cube-shaped blocks = 3375

Volume of one identical cube-shaped block = 3375/27 = 125 in^2

We would find the side length of one identical cube-shaped block

Thus,

125 = s^3

Taking the cube root of both sides,

s = cube root of 125

s = 5

The side length of the blocks is 5 inches

The formula for calculating the surface area of a cube is expressed as

surface area = 6a^2

Surface area of larger cube = 6 x 15^2 = 1350

surface area of each small block = 6 x 5^2 = 150

the total surface area of the 27 blocks = 27 x 150 = 4050 square inches

Ratio of surface area of the 27 blocks to the original box = 4050/1350 = 3

This is 3 times the surface area of the box.



Answer:

25

Step-by-step explanation:

225 divided by 9 is 25

To solve our session let's first illustrate the situation as follows:

As we can see above, W is in the middle of angle XYZ. And we show all the angles in the picture. Once angle XYW + angle WYZ is equal to angle XYZ we can write the following expression and calculate:

So, finally, x = 8 and

Answer:

B

Step-by-step explanation:

41 + 40 + 57.28 ft, 138.28 ft.

the answer is 39 because you do 108 - 147

Answer:

Since we are talking annual interest and, I assume a time period of 1 year:

The interest earned is the sum of the interest earned on the two loans separately

Let x = amount loaned at 14%

18,500-x = amount loaned at 12%

I = prt

p = x and 18500-x

r = 0.14 and 0.12

t = 1

2390 = 0.14x + 0.1(18500-x)

2390 = .14x + 1850 - 0.1x

x = 13500

x = $13,500 loaned at 14%

18500-x = $5,000 loaned at 12%

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Step-by-step explanation:

Total loan: $18,500.

Part at 14%

Part at 12%

Let the part at 14% = x.

Let the part at 12% = y.

Equation of amount of loan:

x + y = 18500

x amount at 14% earns 14% of x = 0.14x interest.

y amount at 12% earns 12% of y = 0.12y interest.

Equation of interest charged:

0.14x + 0.12y = 2390

We have a system of equations.

x + y = 18500

0.14x + 0.12y = 2390

Multiply both sides of the first equation by -0.12. Write the second equation below it, and add the equations.

     -0.12x - 0.12y = -2220

(+)    0.14x + 0.12x = 2390

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

      0.02x             = 170

x = 170/0.02

x = 8500

x + y = 18,500

8500 + y = 18,500

y = 10,000

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Answer:

27

Step-by-step explanation:

The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60

(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.

Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200

Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments

Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]

Total amount paid = $1,300 + $13,200 + $14,041.60

Total amount paid = $28,541.60

Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.

(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.

Total interest paid = Total amount paid - Total amount borrowed - Down payment

Total interest paid = $28,541.60 - $13,200 - $1,300

Total interest paid = $14,041.60

Therefore, the amount of interest Debra paid on the loan was $14,041.60.

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Answer: 21

Step-by-step explanation:

arc AC = 2b

3x + 9 = 2(3x - 1.5)

3x + 9 = 6x - 3

solve for x

6x - 3x = 9 + 3

3x = 12

x = 4

substitute in the 2 equations

3 (4) - 1.5 = 10.5

which means that if we substitute in the second equation we should get 21

3(4) + 9 = 21

so arc AC= 21 degrees

Answer:

d i think

Step-by-step explanation:

Check the picture below.

if the barrel is rolled up the ramp 26 times, each time the barrel is rolled up fully, it covers a length the circumference of its base, so if it does it 26 times, it wen up its base circumference 26 times.

\(\textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=2.5 \end{cases}\implies C=2.5\pi \implies \stackrel{\textit{26 times}}{C =65\pi }\implies \stackrel{\pi =3.14}{C=204.1}\)

Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Rhett's house is a rectangular prism

Given data ,

Let the figure be represented as A

Now , the value of A is

Rhett made a simple drawing of his house.

And , It is a three dimensional figure with four faces that are rectangular and two that are square

So , the figure is represented as a rectangular prism

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Hence , the figure is rectangular prism

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Answer:

3.553 is the answer.

Step-by-step explanation:

Write it down

Answer:

3.553 is bigger

Step-by-step explanation:

If you look at the whole numbers, they are the same (3). Then, you would go to the tenths place, which is 5. Both number's tenths places are 5. Then, you look at the hundredths place. The first has 4 as its hundredths place. The second number has 5 as its hundredths place. 5 is more than 4, so 3.553 is more than 3.544.

The value of x is 58.51 degree.

We have,

Perpendicular= 8

Base = 4.9

Using trigonometry

tan x = Perpendicular/ Base

tan x = 8/4.9

tan x= 1.63265306122449

x = 58.51253064

Thus, the value of x is 58.51 degree.

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Answer:

2 1/6 miles

Step-by-step explanation:

1 1/2 miles + 2/3 miles = 2 1/6 miles

Answer:

780

Step-by-step explanation:

24 - 67 = - 43

- 43 - 88 = - 131

- 131 + 77 - 77 = - 131

- 131 + 78 = - 53

- 53 - 55 = - 108

- 108 + 888 = 780

1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

The given data are: \(22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7\)

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: \(\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8\)

= \(\sqrt{128.3336}\)

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = \(11.3284 ^2\)

Variance = 128.33264656

Variance = 128.33.

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Answer:

1.78f

Step-by-step explanation:

7/4=1.78 and then you add f

Answer:

$30.21

Step-by-step explanation:

100% -25%= 75%

Discounted price of the book

= 75% ×$38

= $28.50

Since the customer must pay an additional 6% of the discounted price,

percentage of discounted price paid

= 100% +6%

= 106%

Total amount paid

= 106% × $28.50

= $30.21

_________________________________

Alternative working:

Original selling price= $38

Since the book is discounted 25%,

100% ----- $38

1% ----- $0.38

75% ----- 75 ×$0.38= $28.50

Since the sales tax is based on the discounted price, we let the discounted price be 100%.

100% ----- $28.50

1% ----- $0.285

106% ----- 106 ×$0.285= $30.21

∴ The total amount the customer pays for the discounted book is $30.21.

Answer:

\(\frac{x-4}{5x}\)

Step-by-step explanation:

The equation;

\(\frac{x^{2} - 8x + 16}{5x}\) ÷ x - 4

Factor;

\(\frac{(x-4)^{2}}{5x}\) ÷ ( x - 4 )

Rewrite in fraction form, so that one can perform division

\(\frac{(x-4)^2}{5x} * \frac{1}{x-4}\)

Simplify, cancel out like terms on opposite sides of the fraction bar

\(\frac{x-4}{5x}\)

Answer:

\(\displaystyle \boxed{W=x+1}\)

Step-by-step explanation:

Area of a rectangle

A rectangle of length L and width W has an area of:

A = L*W

If the area and one of the dimensions are given, we can calculate the other dimension by solving the resulting equation.

The area of the given rectangle is 6x+6 square centimeters, and its length is 6 cm, thus we can establish the equation:

\(6W=6x+6\)

Solving for W:

\(\displaystyle W=\frac{6x+6}{6}\)

The numerator 6x+6 can be factored as 6(x+1). Replacing in the equation:

\(\displaystyle W=\frac{6(x+1)}{6}\)

Simplifying, the width of the rectangle in cm is:

\(\displaystyle \boxed{W=x+1}\)

Answer:

it is ...... x+1

Step-by-step explanation:

I did it your welcome

Answer:

15:20

Step-by-step explanation:

We can simplify the ratio to 3:4

after doing that we can multiply both sides by 5 giving us

                          15:20   as our answer

Or you can cross multiply

9 : 12 = 15 : x

Now we have 9x = 180

divide both sides by 9 and we get

x=20

which would work giving us the ratio of                         9 : 12 = 15 : 20

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer: To graph y = f(x) and y = 1/f(x) on the same axes, you can follow these steps:

First, graph y = f(x) by plotting a few points, such as (-5, -19), (-3, -1), (0, 1) and (5, 19), and then connecting them with a smooth curve.

Then, graph y = 1/f(x) by finding the inverse function of f(x) which will be

1/f(x) = -1/(x+4)²+1

Next, plot a few points on this new function, such as (-5, -1/19), (-3, -1), (0, 1) and (5, 1/19), and then connecting them with a smooth curve.

Finally, make sure that the same x and y scales are used for both graphs, and label the axes and the functions clearly.

It is important to note that as f(x) = -(x+4)²+1, the domain of f(x) is all real numbers but the range is (1, infinity) so the reciprocal will be defined only for the range of f(x) and the domain of 1/f(x) will be (1, infinity)

Also, the graph of y = f(x) will be a parabola opening upwards and y = 1/f(x) will be a parabola opening downwards, both with vertex (-4,1)

The graph of y = -(x+4)²+1 will be a parabola opening upwards and the graph of y = -1/(x+4)²+1 will be a parabola opening downwards.

Step-by-step explanation:

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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