In recent years, Sheffield Transportation purchased three used buses.

Answer:

82 in^2

Step-by-step explanation:

Total Surface Area (TSA) = 2 × Base Area + Base Perimeter × Height

TSA = 2× (7×2) + (7+7+2+2) ×3

= 2 × 14 + 18 × 3

= 82 in^2

The quotient evaluated in 7 is equal to the quotient of the two functions evaluated in 7, thus:

(f/g)(7) = f(7)/g(7) = 3

Here we know the functions:

f(x) = 2x + 1

g(x) = x - 2

The quotient evaluated in 7 is equal to the quotient between the two functions evaluated in x = 7, then here we will get:

f(7) = 2*7 + 1 = 14 + 1 = 15

g(7) = 7 - 2 = 5

Then the quotient gives:

(f/g)(7) = f(7)/g(7) = 15/5 = 3

That is the value.

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When we apply Gauss- Jordon elimination method to solve the system of equation, it becomes;

[tex]\left[\begin{array}{cccc}1&0&0&6\\0&1&0&2\\0&0&1&-6\end{array}\right][/tex]

To solve the augment matrix that represents a system of linear equation using Gauss- Jordon elimination method, we reduce every value to 0's and 1's to get the values in the fourth column.

-5   -3    -4   -12

0    -2    -7    38

0      1     4    -22

    R₁ ÷ -5                                   R₂ ÷ -2

1    3/5     4/5  12/15             1    3/5    4/5   12/15

0    -2    -7    38                   0     1       7/2   -19

0      1     4    -22                  0      1     4    -22          

R₁ - 3/5R₂                                   2R₃

1      0   -13/10   69/5              1      0   -13/10   69/5

0     1      7/2     -19                 0     1      7/2     -19

0     0     1/2      -3                   0     0     1         -6

 R₂ + 13/10R₃                                  R₂ - 7/2R₃

1      0     0     6                             1      0     0     6  

0     1      7/2  -19                          0     1      0      2

0     0     1         -6                         0     0     1      -6

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Answer:

Step-by-step explanation:

You want to find the values of cos(x), tan(x), and sin(x) in right triangle DEF as shown in the figure.

The relationships between trig functions and sides of a right triangle are summarized in the mnemonic SOH CAH TOA. This tells you ...

  Cos = Adjacent/Hypotenuse

  cos(x) = f/e

  Tan = Opposite/Adjacent

  tan(x) = d/f

  Sin = Opposite/Hypotenuse

  sin(x) = d/e

<95141404393>

Answer:

1/6

Step-by-step explanation:

1 x 1/6 = 1/6

Any number multiplied with one is that number itself.

1/6

Step-by-step explanation: Anything multiplied by 1 equals itself, therefore, the answer is 1/6. Hope this helps, and please give me Brainliest! :)

Step-by-step explanation:

The value of the digit 1 in the number 213,456 is 10,000.

The total area of the figure is 50.13 square units.

We can decompose the figure into a rectangle of 12 by 3 units, and a semicircle whose radius is 3 units.

Remember that the area of a rectangle is equal to the product between its dimensions, then the area of the rectangle we will get.

A = 12*3 = 36 square units.

For a semicircle of radius R, the area is:

a = 0.5*3.14*R²

Here the radius is 3 units, then.

a =  0.5*3.14*3² = 14.13 square units.

Adding that we will get:

total area = 36 square units + 14.13 square units.

total area = 50.13 square units.

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Answer:

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

Tangent is perpendicular to radius, hence ΔAOB is right triangle.

Given that OA = AB, and we know OA = OC as two radius. Therefore OAC is equilateral triangle, hence all its angles are same:

It means ΔOAB is a specific 30x60x90 right triangle.

The ratio of its sides is:

It gives us that:

Answer:

Step-by-step explanation:

You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.

We can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...

These equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.

We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...

__

Additional comment

Using b = c +10000, the two remaining equations are ...

<95141404393>

The specific measurements or Dimensions of the cone and cylinder (such as the radius and height).

The volume of the component part consisting of a cone on top of a cylinder,  the volumes of the individual shapes and sum them together. the part consists of a cone and a cylinder/

1. Volume of the cone:

The volume of a cone can be calculated using the formula V_cone = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height of the cone.

2. Volume of the cylinder:

The volume of a cylinder can be calculated using the formula V_cylinder = π * r^2 * h, where r is the radius of the base and h is the height of the cylinder.

the given diagram and determine the necessary measurements. without the specific measurements or dimensions (such as the radius and height of the cone and cylinder), I am unable to calculate the volumes.

the specific measurements or dimensions of the cone and cylinder (such as the radius and height).

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Answer:

       0      1      2      3      4      5      6      7

       |      |      |      |      |      |      |      |

     2/3   1     2.7    3.4         7      |

                         |_____________|

                               |

                             3 3/4

The simplification of the given expression above would be = x⁵

The exponential laws in mathematics states that to multiply two exponential functions with the same base, we simply add the exponents.

The second law states that to divide two exponential functions with the same base, we subtract the exponents.

From the expression given above;

x⁷/x² = X(7-2) = x⁵

Therefore, in conclusion, the simplification of the given expression above while following the guide of the exponential laws would be = x⁵

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Answer:

To find the x-intercepts, we set y = 0 and solve for x:

f(x) = (x+9) (x+9) (x-8) = 0

The solutions are x = -9 (double root) and x = 8.

To find the y-intercept, we set x = 0:

f(0) = (0+9) (0+9) (0-8) = -583.

Therefore, the y-intercept is (0, -583).

Answer: $28.00 (C)

Step-by-step explanation:

The total is 28 (based on the equation).

No matter how many blueberries or raspberries Amit buys, the toal must equal 28 dollars.

The numeric value of the derivative at x = 3 is given as follows:

C. 0.5.

The quotient function has the format given as follows:

(f/g)(x).

The derivative of the function is obtained applying the quotient rule, as follows:

(f/g)'(x) = [f'(x)g(x) - f(x)g'(x)]/[g(x)]².

Then at x = 3, the derivative is given as follows:

(f/g)'(3) = [f'(3)g(3) - f(3)g'(3)]/[g(3)]².

Replacing the values from the table, we have that:

(f/g)'(3) = [3 x 2 - 1 x 4]/2².

(f/g)'(3) = 2/4

(f/g)'(3) = 0.5.

Meaning that the correct option is given by option C.

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The fountain will occupy a fraction of 50/173 of the Total area of the courtyard.

Let A be the area of the courtyard and F be the area of the fountain.

We know that the area of the stone-covered part of the courtyard is 246 square feet.

So, the area of the whole courtyard is A = 246 + F square feet.

The fraction of the area of the courtyard occupied by the fountain is given by:

F / A = F / (246 + F)

We can simplify this expression by multiplying the numerator and denominator by the reciprocal of the denominator:

F / A = F / (246 + F) * (1 / (246 + F))

F / A = F / (246 * (246 + F))

F / A = 1 / (246 / F + 1)

We don't know F yet, but we can use the fact that the fountain is rectangular to set up an equation relating the length and width of the fountain:

F = L * W

where L is the length of the fountain and W is the width of the fountain.

We also know that the perimeter of the fountain is 50 feet:

2L + 2W = 50

Simplifying this equation, we get:

L + W = 25

Solving for one variable in terms of the other, we get:

L = 25 - W

Substituting this expression for L into the equation for F, we get:

F = (25 - W) * W

Expanding this expression, we get:

F = 25W - W^2

We also know that the cost of the fountain is $600, which includes installation. So, we can set up another equation relating the cost of the fountain to its dimensions:

1.5LW = 600

Substituting 25 - W for L, we get:

1.5(25 - W)W = 600

Expanding and simplifying this equation, we get:

W^2 - 25W + 400 = 0

Solving this quadratic equation, we get:

W = 20 or W = 5

We reject the solution W = 5 because it implies a negative length for the fountain, which is not physically possible. Therefore, the width of the fountain is W = 20 feet and its length is L = 25 - W = 5 feet.

The area of the fountain is therefore:

F = L * W = 5 * 20 = 100 square feet

The fraction of the area of the courtyard occupied by the fountain is

F / A = 100 / (246 + 100) = 100 / 346 = 50 / 173

So, the fountain will occupy a fraction of 50/173 of the total area of the courtyard.

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13

5^2+12^=169

square root of 169=13

if the triangle wasnt a right angled triangle it would equal to 13 and would give u something else

The amount more in income tax that Cho pays than Helen each month would be £56.

Here, we have,

First, find Helen's yearly salary :

= 1, 720 x  12

= £ 20, 640

Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.

Cho 's monthly tax would be:

= (( 24, 000 - 12, 570 ) x 20 % ) / 12

= £ 190. 50

Helen's monthly tax :

= (( 20, 640 - 12, 570 ) x 20 % ) / 12

= £ 134.50

The difference is therefore :

= 190. 50 - 134.50

= £56

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complete question:

You can use these steps to work out the amount of income tax you pay each month.

Work out

monthly salary - 987.5

Work out

answer to Step 1 +5

Step 1

Step 2

Cho has a salary of £24 000 per year.

Helen has a salary of £1720 per month.

How much more income tax does Cho pay than Helen each month?

The value of the hypotenuse AB is 4.73 units.

Given is right triangle, we need to find the measure of side AB,

So, we know that the Sine of an angle is the ratio of the perpendicular side to the hypotenuse of the triangle,

So,

Sin A = BC / AB

Sin 25° = 2 / AB

AB = 2 / Sin 25°

AB = 4.73

Hence the value of the hypotenuse AB is 4.73 units.

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The number of balloons needed to fill the room is given as follows:

5729 balloons.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions of the room are given as follows:

15 ft, 25 ft and 8 ft.

Hence the volume is given as follows:

V = 15 x 25 x 8

V = 3000 ft³

The volume of a sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

V = 4πr³/3.

The balloon has a radius of 0.5 ft, hence it's volume is given as follows:

V = 4π x 0.5³/3

V = 0.5236 ft³.

Then the number of balloons is obtained as follows:

3000/0.5236 = 5729 balloons.

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Hello,

150 - 1/3% of 150

= 150 - 33,33% x 150

= 150 - 50

= 100

approximately 100

Example: 33 1/3% = 1/3. 1/3 of $150.00 = $50.00, so discounted price is: $150.00 - $50.00 = $100.00

Five-number summary for data set A is: 21, 23.5, 27, 31.5, 34

Five-number summary for data set B is: 21, 22.5, 24.5, 28.5, 35

the five-number summary of a data set consists of:

The minimum or the lowest value

First quartile (Q1), that is the middle of the first part of the data set when ordered.

Median, that is the center of the data set.

Third quartile (Q3), that is the middle of the second part of the data set when ordered.

Maximum value or largest value.

The five-number summary is written from the least to the largest value.

Five-number summary for data set A:

Given, 24, 31, 30, 32, 23, 25, 34, 32, 25, 21, 22, 29;

Minimum: 21

First Quartile: 23.5

Median: 27

Third Quartile: 31.5

Maximum: 34

Five-number summary for data set B:

Given, 35, 33, 32, 21, 22, 23, 24, 25, 24, 22, 25, 25;

Minimum: 21

First Quartile: 22.5

Median: 24.5

Third Quartile: 28.5

Maximum: 35

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The hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.

The half-life of cobalt-60 is 5.24 years, which means that after 5.24 years, the radioisotope activity will have decreased to 50% of its initial level. Since the hospital needs to replace the cobalt when the radioisotope activity has decreased to 45% of its initial level, this means that the cobalt needs to be replaced after slightly less than one half-life has passed.
To find out how long this is, we can use the formula:
t = (ln(0.45) / ln(0.5)) x 5.24
where t is the time in years since the cobalt was first used.
Using a calculator, we find that:
t ≈ 2.16 years
Therefore, the hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.

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Her savings would be $12.72 ($760 - $744.80 - $2.48).

The difference in the final payment is therefore $221.50 - $150 = $71.50.

a. The printer's price after the trade discount is $760 ($860 - $100). If Janet takes the 2% cash discount, she'll pay $744.80 ($760 * 98%).

If she borrows this amount at 6% for 20 days (the difference between 30 days credit and 10 days cash discount), her interest cost will be $2.48 ($744.80 * 6% * 20/360).

Therefore, her savings would be $12.72 ($760 - $744.80 - $2.48).

b. For choice 1, Janet would pay $150 for 17 months and then the remainder ($4,020 * 75% - $150 * 17) in the 18th month.

For choice 2, the monthly payment is $221.50, calculated by using the formula for an installment loan.

The difference in the final payment is therefore $221.50 - $150 = $71.50.

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The value of f(3) in the function is undefined

The given function are f(x)= x³+18x²+104x+192 for x≤-3

f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3

f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3

f(x)=√x²-9

We have to find the value of f(3)

The 3 lies in the interval -3< x≤3

So we use function f(x)= 3x-9/x³-2x²-5x+6 to find f(3)

f(x)= 3(3)-9/(3)³-2(3)²-5(3)+6

=0/27-18-15+6

=undefined

Hence, the value of f(3) in the function is undefined

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Answer:100

Step-by-step explanation:

1. The final velocity is 8.3 m/s and the distance covered is 16.8 m.

2. The acceleration is  34.7  and it would travel  58.9 m.

Acceleration is a physical quantity that describes the rate of change of an object's velocity over time. In other words, it is the rate at which the speed or direction of motion of an object changes.

Using;

v = u + at

v = ?

u = 2.9 m/s

a = 1.8 m/s2

t = 3 s

Then;

v = 2.9 + (1.8 * 3)

v = 8.3 m/s

Also;

[tex]v^2 = u^2 + 2as\\s = v^2 - u^2/2a\\s = (8.3)^2 - (2.9)^2/2 * 1.8[/tex]

s = 68.89 - 8.41/3.6

= 16.8 m

2)

[tex]v^2 = u^2 + 2as\\a = v^2 - u^2/2s\\a = (27)^2 - 0^2/2 * 10.5[/tex]

a = 34.7[tex]m/s^2[/tex]

Using;

[tex]s = ut + 1/2at^2\\ut = 0\\s = 1/2at^2\\s = 0.5 * 34.7 * (2)^2\\s = 69.4 m[/tex]

It would travel; 69.4 - 10.5 = 58.9 m

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