If housekeeping normally takes 10 minutes to prepare a patient’s room, how many rooms can one housekeeper be expected to handle in an 8 hour shift

Step-by-step explanation:

speed = distance / time

to get distance, we have to multiply by time.

the speed the 2 busses are moving seat from each other is

x + (x + 17) = 2x + 17

x = the speed of one bus

x + 17 = the speed of the other bus.

so, after 4 hours the distance between them is

(2x + 17) × 4 = 836

2x + 17 = 209

2x = 192

x = 96 km/h

bus 1 travels at 96 km/h.

bus 2 travels at 96+17 = 113 km/h.

The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.

The identity is presented as follows:

[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]

Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:

[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]

The following identity relates the square of the secant and of the tangent:

[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]

Hence:

[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]

Thus the remaining expression is:

[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]

The equations of the cotangent, secant and tangent are given as follows:

Hence:

[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]

One divided by the sine is the cosecant, as follows:

[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]

Hence the simplified expression is:

[tex]\csc{\beta} + 1[/tex]

Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.

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Answer: y+7=-4(x-2)

Answer: y+7=-4(x-2)

Answer:

y=4x+14

Step-by-step explanation:

The multiplication of the given function is  (fg)(x) = 12[tex]x^3[/tex]

What is operations of the function ?

   Similar to how a function's constituent terms can be added, subtracted, multiplied, and divided, so can functions. These are to be noted as follows:

Addition f( x ) + g ( x ) means to combine two functions, and it may alternatively be expressed as ( f + g ) ( x )

It is possible to write ( f g ) ( x ) to represent the operation of subtracting the g(x) function from the f(x) function.

The two functions are multiplied together when you multiply f (x ) g (x), which can also be represented as (f g ) (x).

Division f (x)/g (x) means to split the two functions in half, and it can alternatively be expressed as (f/g)(x).

Here the given function ,

=> f(x) = 4[tex]x^2[/tex]

=> g(x)= 3x

Now (fg)(x) = f(x)*g(x)

=> (fg)(x)=  4[tex]x^2[/tex]*3x

=>  (fg)(x) = 12[tex]x^3[/tex]

Hence the  (fg)(x) = 12[tex]x^3[/tex].

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For isosceles triangle RST  the measure of angle T is 34 degree

In this question, we have been given a isosceles triangle RST with RS = RT.

So, by isosceles triangle theorem,

angle S = angle T

So, angle T = (3x - 2)°

We know that the sum of all angles of triangle is 180°

∠R + ∠S + ∠T = 180°

9x + 4 + 3x - 2 + 3x - 2 = 180°

15x + 4 - 4 = 180°

15x = 180°

x = 12

So, 3x - 2 = 3(12) - 2

                = 34°

Therefore, for triangle RST  the measure of angle T is 34 degree

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Answer:Say w= the amount of water in oz, then the 60% of the solution is 250 - w

Set up the equation:

Use distributive property first

0.60(250-w) = 0.15 x 250

Isolate to solve for w

150- 0.60w= 37.5

-0.60w= 37.5-150

0.60w= -112.5

w= 187.5 ounces

250-187.5= 62.5 ounces salt solution



Therefore, she must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.

Hope this helps!

Step-by-step explanation:

The 30 feet by 15 feet dimension of the old stage and the 1,000 square feet of the new stage generates equations that gives the depth of the new stage;

An equation states the relationships between two expressions as being of the same value.

The width and depth of the concert hall for the old stage are 30 feet and 15 feet respectively

Area of the new stage = 1000 ft.²

The dimensions of the new stage are;

Width = 30 + x

Depth = 15 + x

Which gives;

(30 + x) × (15 + x) = 1,000

(30 + x) × (15 + x) - 1,000 = 0

x² + 45·x - 550 = 0

(x + 55)·(x - 10) = 0

The distance added to the width and length of the old stage, x = 10

The width of the new stage = 30 feet + 10 feet  = 40 feet

The depth of the new stage = 15 feet + 10 feet = 25 feet

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The given points gives us a line with constant slope of -2.

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

The points are in the form of ( x, y) , where y= g(x)

Plot these points on the graph and join the points through a line.

Refer to the attachment for the graph.

The slope is constant.

consider any 2 points:

(x,y) = (0,7)

(m,n) =(2,3)

Slope = change in y values/ change in x values

         = (7-3)/(0-2) = 4/-2 = -2

The given points gives us a line with constant slope of -2.

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The probability that the sum is 5/9.The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa).

The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa). Given that this is feasible 4 times out of 36, the probability calculated by adding the two dice is 4/36, or 1/9.

I am assuming that you are rolling two dice.

Probability of even: 18 "evens" out of 36 total outcomes = 18/36

→(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5),(4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

Probability of greater than 9: 6 ">9s" out of 36 total outcomes = 6/36

→(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)

Probability of both evens and >9s: 4 "both" out of 36 total outcomes = 4/36

→(4,6), (5,5), (6,4), (6,6)

evens   OR    >9s    NOT both

18/36 + 6/8 - 4/36 = 20/36 = 5/9.

The probability that the sum is 5/9.  

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]

The length of the second rectangle is 8 in

Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where

So, making Wsubject of the formula, we have

W = A/L

Since

Substituting these into the equation, we have

W = A/L

W = 48 in²/6 in

W = 8 in

Now, since the  second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where

So, making L subject of the formula, we have

L = A/W

Since

Substituting these into the equation, we have

L = A/W

L = 64 in²/8 in

L = 8 in

So, the length of the second rectangle is 8 in

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Answer:

-3

Step-by-step explanation:

we sure y2-y1/x2-x1 to find slope

6+6/-4+0

12/-4

-3 is the slope

Hopes this helps please mark brainliest

For the given polynomial the degree is 1, the leading coefficient is 1, and the constant term is 5.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The given polynomial is x+5.

(1) The degree is the highest power of the polynomial.

Degree = 1

(2) The leading coefficient is 1.

(3) The constant term is 5

Therefore, the given polynomial degree is 1, the leading coefficient is 1, and the constant term is 5.

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Answer:

  (2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333

Step-by-step explanation:

You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.

The graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².

The area will be the product of the width and height:

  A = WH

  A = (2x)(5 -x²) = 10x -2x³

The area will be a maximum where the derivative of the area function is zero.

  dA/dx = 10 -6x² = 0

  x² = 10/6

  x = (√15)/3

The corresponding rectangle dimensions are ...

  width = 2x = (2/3)√15

  height = 5 -x² = 5 -5/3 = 10/3

The rectangle with largest area is (2/3)√15 wide by 10/3 tall.

Answer:

IT IS A FUNCTION

It is specifically a Surjective/ onto Mapping/function

Step-by-step explanation:

surjective or onto function is when y has an image in x

Answer:

The graph is a function

Step-by-step explanation:

-For every input (x) there is only one output value (y)

Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.

Ex.

X: 2, 4, 7 , 2, 5         This is not a function. More than one input for each output.

Y: 1, 2, 4, -3, 7

Ex.

X: 5, 6, -5, 8  this is a function. Exactly one input for every output.

Y: 1, 4, 5, 9

The number of kilograms that the crane is lifting, based on the maximum it can lift and the proportion being lifted is 160 kilos

The number of kilos that the crane is lifting can be found by the formula :

= Maximum kilogram capacity x Proportion of maximum being lifted

Maximum kilogram capacity = 224 kg

Proportion of maximum being lifted = 5 / 7

The kilos being lifted by the crane is therefore :

= 224 x 5/7

= 1, 120 / 7

= 160 kilos

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Answer:

20

Step-by-step explanation:

Absolute value is the distance from zero. Absolute value is always positive.

| -20 | is positive. It is 20 units from 0. So it is 20.

| -20 | = 20

(Be careful, absolute value doesn't just flip the sign to the opposite.

| 20 | = 20 also because the distance from 0 to 20 is also 20.)

The marginal cost is the labor utilized in order to provide an additional cost of a haircut.

The marginal cost is the extra cost of generating one additional unit of output.

The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.

Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.

Change in cost / Change in quantity Equals Marginal cost.

The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.

Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.

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Step-by-step explanation:

a + b + c + d = 125

a + 4 = b - 4 = 4c = d/4

a + 8 = b

a = b - 8

16c = d

b = 4c + 4

4a + 16 = d

b - 8 + 4c + 4 + c + 16c = 125

4c + 4 - 8 + 4c + 4 + c + 16c = 125

25c = 125

c = 5

d = 16c = 80

4a + 16 = d = 80

4a = 64

a = 16

b = a + 8 = 16 + 8 = 24

so, the numbers are

16, 24, 5, 80

Answer:

x° = 34°

Step-by-step explanation:

First, find the interior angle supplementary to the given exterior angle 124°.

I will label it y.

124° + y° = 180°

y° = 180° - 124°

y° = 56°

Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.

x° + y° + 90° = 180°

x° + y° = 90°

x° + 56° = 90°

x° = 90° - 56°

x° = 34°

Answer:

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

Answer:

Step-by-step explanation:

570.675

Answer:

x = -32/31

Step-by-step explanation:

4x - 1/8 x = -2 -2

(32 - 1)/8 x = -4

31/8 x = -4

x = -4 * 8/31

x = -32/31

Answer:

[tex]\frac{7}{4}[/tex] or 1 [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

I am not sure if you meant 6x or 6+x at the end of the equation. I went with what was written.

5x -3(x-3) = -5 +4x +6x  Distribute the -3

5x -3x + 9 = -5 + 4x + 6x  Combine like terms

2x + 9 = -5 + 10x  Subtract 2x from both sides

9 = -5 + 8x  Add 5 to both sides

14 = 8x  Divide both sides by 5

[tex]\frac{14}{8}[/tex] = x

[tex]\frac{7}{4}[/tex] o r 1 [tex]\frac{3}{4}[/tex]

In the proportional relationship table, x would represent distance and y, weight.

The complete table is given in the explanation below.

If two variables that have quantities that vary proportionately are x and y, then the constant of proportionality that lies between both varies can be calculated as k = y/x. The equation for the proportional relationship would be expressed as y = kx.

x represents distance (cm)

y represents weight (newtons).

Using the pair of value that is given in the table, (20, 28), the constant of proportionality, k, would be:

k = y/x = 28/20

k = 1.4

The equation would be y = 1.4x.

Use the equation to complete the table by substituting the value of each missing variables:

Row 2, when x = 55:

y = 1.4(55)

y = 77

Row 3, when y = 140:

140 = 1.4x

140/1.4 = x

100 = x

x = 100

Row 4, when x = 1:

y = 1.4(1)

y = 1.4

The table would be:

           Distance (cm)     Weight (newtons)          

Row 1        20                     28

Row 2       55                     77

Row 3       100                    140

Row 4        1                        1.4              

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Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.

In the given question,

The measurements of two sides of a triangle are 12 cm and 17 cm.

We have to find which side length could be the measurement of the third side of the triangle.

We know that,

The sum of the length of any two sides is always greater than the third side.

The given sides of triangles are 12 cm and 17 cm.

Hence, the length of the third side should be shorter than the total of the other two sides,

12 + 17 = 29 cm.

Considering that the third side must be less than the difference between the first two sides,

17 – 12 = 5 cm

So, the length of the third side falls between 5 cm and 29 cm.

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Step-by-step explanation:

10 hours per week: $10.50 x 10 = $105.00

20 hours per week: $105.00 x 2 = $210.00

40 hours per week: $210.00 x 2 = $420.00