The doctor orders 100 units of a medication to administer daily. The vial is labeled 50 units/mL. How many mL will be administered if the patient stays in the hospital for a week?

The equation of a line perpendicular to y = -3/4x +1 and passes through (12, 9) is y = 4  /3 x - 7

A linear graph can be represented in slope intercept form as follows:

y = mx + b

where

The line passes through the points (12, 9) and its perpendicular to the graph y = -3/4x +1.

The products of the slope of perpendicular lines is equals to negative one.

Therefore,

m₁ m₂ = -1

Hence,

- 3 / 4 m₂ = - 1

cross multiply

-3m₂ = -4

m₂ = 4 / 3

Therefore, let's find the y-intercept of the line using (12, 9)

y = 4 / 3 x + b

9 = 4  /3(12) + b

9 = 16 + b

b = 9 - 16

b = - 7

Therefore, the equation of the line is y = 4  /3 x - 7

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The inequality - 3(2x - 5) < 5(2 - x) is x > 5 represents a line with an open circle at x = 5 and going indefinity to positive infinity.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, inequality is  - 3(2x - 5) < 5(2 - x).

∴ - 6x + 15 < 10 - 5x.

- 6x + 5x < 10 - 15.

- x < - 5.

x > 5   (think of moving x to the other side to make it positive.

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Answer:

choose 3rd option

Step-by-step explanation:

The total sum of money shared is $4800

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b

The ratio of mark to Mary to gabrielle is 3:5:8

this means the total ratio is 16 i.e 3+5+8=16

if the total money is y and the money shared to mark is x, then

3/16× y= x

therefore 3y=16x

y= 16x/3 equation 1

Mary receives 600 more than mark,this means Mary share = 600+x

therefore 5/16×y= 600+x

5y= 16(600+x)

5y= 9600+16x equation 2

substitute 16x/3 for y in equation 2

5×16x/3= 9600+16x

80x/3= 9600+16x

multiply both sides by 3

80x= 3(9600+16x)

80x= 28800+48x

collect like terms

80x-48x= 28800

32x=28800

x= 900

substitute 900 for x in equation 1

y=16×900/3

y= 4800

therefore the total money shared is 4800

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The difference between Prince George's County's population (908,670) and Charles county (159,428) is 749,242.

To find the difference between two values, we use the mathematical operation of subtraction.

Subtraction operation involves the use of the minuend, subtrahend, difference, and equation sign.

The subtrahend is the number deducted from the minuend, to get the difference.

  908,670 ... minuend

-  159,428 ... subtrahend

= 749,242 ... difference

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Kala the trainer lasted 0.75 hours for each of the work out.

Let A represent plan A and B for plan B

On Wednesday there were 3 clients who did Plan A and 5 who did Plan B for a total of 6 hours. this is represented mathematically as

3A + 5B = 6 hours

On Thursday there were 9 clients who did Plan A and 7 who did Plan B for a total of 12 hours. this is represented mathematically as

9A + 7B = 12 hours

hence we have two system of equations with two unknown

9A + 7B = 12 hours

3A + 5B = 6 hours

solving the equation gives that A = B = 0.75 hours = 45 minutes

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The effective tax rate is 24%  for a taxable income of $75,400

The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate.

the"marginal" income is what is taxed at the next highest tax bracket as moves up in tax brackets, this tax rate is known as the marginal tax rate.

Given that;

Marginal Tax Rate           Chart Tax Bracket

$0 –$10,275                                  10%

$10,276 –$41,175                           12%

$41,176 –$89,075                          22%

$89,076 –$170,050                      24%

$170,051 –$215,950                      32%

$215,951 –$539,900                     35%

> $539,901                                     37%

Thus, the effective tax rate for income of $95, 600 lies in the range of a marginal tax rate of 24%.

So, the effective tax rate;

= 72,026/ 95600

= 24 %

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Answer:

16.27%

Step-by-step explanation:

Hello,

10275 ×  10% = 1027.5

41175 - 10276 = 30899

30899  × 12% = 3707.88

Then we would input 75400 since it fits in to ($41176–$89075)

75400 - 41176 = 34224

34224 × 22% = 7529.28

Then we would add it all up

1027.5 + 3707.88 + 7529.28 = 12264.66

Then to determine the effective tax rate for 75400 we would

 [tex]\frac{12264.66}{75400}[/tex] × 100 = 16.27%

So, the effective tax rate for the taxable income of 75400 is 16.27%.

Answer:

a)  Intersecting lines.

b)  Parallel lines.

c)  Skew lines.

d)  Intersecting planes.

e)  Parallel planes.

Step-by-step explanation:

A prism is a polyhedron that has:

From inspection of the give diagram, the figure appears to be a triangular prism with triangular bases ADE and BCF.

Lines

Planes

A plane is a flat, two-dimensional surface that extends into infinity.  

A plane can be named by the letters naming three non-collinear points in the plane.

a)  AB and BC are intersecting lines as they share the common point B.

b)  AE and BF are parallel lines because they both lie on the plane ABF, do not intersect and are the same distance apart.

c)  EF and AD are skew lines because the do not lie on the same plane, they do not intersect and they are not parallel.

d)  Plane ABC and plane ABF are intersecting planes as they intersect along line AB.

e)  Plane AED and plane BFC are parallel planes as they are the bases of the prism and never intersect.

The company's expected cash receipts for August from its current and past sales is $126220.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the sales for June, July, and August are $56000, $62000, and $52000 respectively.

The company collects 45% of sales in cash, therefore, for June month the cash collected by the company is,

June = 56000×45%

June =56000×45/100

June =25200

Therefore, the credit amount for June is,

56000 - 25200

=30800

The cash collected by the company for July is,

= 62000×45%

=  62000×45/100

= 27900

The company will also collect 60% of its credit from June sales in July, therefore, the total collected cash in July is,

July  = 27900 + 60% of 30800

July = 27900 + 60×30800/100

July = 46380

The remaining credit after July is,

62000-27900

= 34100

The cash collected for August is,

52000×45%

= 52000×45/100

= 23400

The company also collects cash credits in June and July. Therefore, The net cash collected by the company is,

August = 23400 + 30800×35% + 34100×60%

August = 23400 + 30800×35/100 + 34100×60/100

August = 23400 + 10780 + 20460

            = 54640

Therefore, the total cash collected by the company for august from its current and past sales is,

June + July + August

= 25200 + 46380 + 54640

= 126220

Hence, the company's expected cash receipts for August from its current and past sales is $126220.

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Answer:

with 12 students 3 fear spiders and other while 1 fear of snake and one of dogs. Some fear of all four

Step-by-step explanation:

hey hon, you were not very specific with what you teacher wanted but this is what i got hope it helps!!!!

The relationship of the battery represent a proportional relationship and the constant is 7.7 pounds.

From the information, 6 car batteries weigh 46.2 pounds. The weight per battery will be:

= 46.2 / 6

= 7.7 pounds

Also, rourteen car batteries weigh 107.8 pounds, the weight per battery will be:

= 107.8 / 14

= 7.7 pounds

The constant of proportionality is 7.7.

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The area of the given triangle is 10 square units.

We have a triangle. The vertices of the triangle are J (-2, 1), K (0, 3), and L (3,-4). We need to find the area of the triangle. We will use the determinant method to calculate the area of a triangle if the coordinates of the vertices are given. If the vertices of a triangle are (x1, y1), (x2, y2), and (x3, y3), then the formula for the area of the triangle is given below.

A = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

A = (1/2)|-2(3 - (-4)) + 0(-4 - 1) + 3(1 - 3)|

A = (1/2)|-2(3 + 4) + 0(-5) + 3(-2)|

A = (1/2)|-14 + 0 + -6|

A = (1/2)|-20|

A = 10

Hence, the area of the triangle is 10.

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The point where the gradient line intercepts (touches) the y-axis is called y intercept.

The point where the gradient line intercepts (touches) the x-axis is called x intercept.

check the sketch attached.

Answer:yes its 15

Step-by-step explanation:

Answer:no

Step-by-step explanation:

No because 2 5's in x

Step-by-step explanation:

area of parallelogram = length × height

780 = 26 × height

height = 780/26 = 30cm

Using system of equation, we can determine that Kadeesha played 10 games and went on 5 rides.

System of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Let;

2.50x + 4.75y = 48.75 ...eq(i)

x = 2y ...eq(ii)

Solving equation (i) and (ii)

x = 10, y = 5

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Answer:

Step-by-step explanation:

so we need slope intercept form, which is  y=mx+b  ... just memorize this, you'll need it many many times

next we are told to find a line perpendicular to y= [tex]\frac{1}{8}[/tex]x+10

recall that the reciprocal of the slope will give us a perpendicular line with a sign change also.

then the slope m is:

m = -8

and we are given the point P(x1,y1) = (  -1,1)

now use the point-slope formula to find the equation to the line in the slope intercept form.

y-y1 = m(x-x1)

plug in our given info.

y-1 = (-8)(x-(-1))

y-1 = -8(x+1)

y-1= -8x -8

y = -8x -8+1

y=-8x-7

there is your slope intercept form of the equation  :)

Answer:

is more than 90 degrees right angles are 90 degrees

Answer:
5d≤20

4 kilometers

Step-by-step explanation:

pls mark

The polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.

Given:

polynomial function s(x) if s(−5)=−4 .

x = -5 when substitute in s(x) the output is -4 which is not equal to zero so

x+5 is not a factor of s(x) is correct.

The factor theorem tells you that a polynomial f(x) has a factor (x - k) only when f(k)=0 . So if s(-5) is not 0, we can draw the conclusion that (x+5) is not a factor of s(x).

Therefore the polynomial function s(x) if s(−5) = −4 is a) x+5 is not a factor of s(x) is the correct option.

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The bicycles which the shop should build to minimize the average cost per bicycle is 25 bicycles

Average cost function:

This is a quadratic function, So

Average cost is minimum when

x = - b / 2a

= -(-0.1) / 2(0.2)

= 0.1 / 0.4

x = 1/4

Number of bicycles which should to minimize average cost per bicycle = minimum average cost × total cost

= 1/4 × 100

= 25 bicycles

Therefore, the number of bicycles which will minimize the average cost function is ,25 bicycles.

Complete question:

Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-0.1x+3.799, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

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The equation of the line that best describes the given table of ordered pair is y = x + 7

Equation of the line:

By using the slope and y intercept of the point, we can calculate the equation of the line as

y = mx + c

here m refers the slope and c refers the intercept.

Given,

Here we have the table of ordered pairs shows the coordinates of the two points on the graph of a line.

Now, we need to find the equation of the line that best suits this one.

In order to find the equation of the table, first we have to calculate the slope and the y intercept of the given table.

But in order to calculate the slope we need the points.

So, the point take has been taken by the table are

=> (-5, 2) and (0,7)

Now, the slope of the line is,

=> m = (0 - (-5))/ (7-2)

=> m = 5/5

=> m = 1

By looking into the point we have identified that the y intercept is 7,

Therefore, the equation of the line is

=> y = 1x + 7

=> y = x + 7

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Answer: 2.3x is the answer

The expression we get from the given functions r and s defined for all real numbers x.

r( s(-3))= -38

Given that,

All real numbers x are defined by the functions r and s.

r(x) =2x+1

s(x) =-2x²-2

We have to find the expression

r( s(-3))

Take the functions,

r(x) =2x+1

s(x) =-2x²-2

Now, Take

r( s(-3))

Substitute s function first

r(-2(-3)²-2)

r(-2(9)-2)

r(-18-2)

r(-20)

Now substitute r function

2(-20)+2

-40+2

-38

Therefore, The expression we get from the given functions r and s defined for all real numbers x.

r( s(-3))=-38=

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The function notation that represents the value of the television after x years is V(x) = 2100 - 235x

You have just bought a new Sony 55'' 3D television set for $2100. The TV value decreases at a rate of 235 dollars per year.  

The linear function to represent the value of the television after x years can be calculated as follows:

Linear equation in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, using function notation, the linear function of the situation is as follows:

V(x) = 2100 - 235x

where

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The expression to represent the average rate of Priya is (5.6×2)÷13 and the average rate is approximately  0.86 miles per hour .

Laura jogs for 2 hours at the rate of 5.6 miles per hour.

Distance travelled = speed × time

= 5.6 × 2

= 11.2 miles

Priya jogs the same distance in 13 hours.

Now to calculate the average rate of Priya we haver to divide the total distance travelled by the total time taken to complete the journey.

Average rate of Priya:

= 11.2 / 13

= 0.86153

≈ 0.86 miles per hour

You will be better able to appreciate the pace of a journey if you are aware of average speed. The speed may occasionally fluctuate while travelling. The need of determining the average speed then increases in order to estimate how quickly the trip will be completed.

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