Convert.
800 oz = lb

subtract 14 from 22 to isolate the variable

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

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Answer:

izoom out,its too close

Answer:

5(5c + 7)

Step-by-step explanation:

Common factor of 25 and 35:

5

Simplified:

5(5c + 7)

The completed entries is added as an attachment

From the question, we have the following parameters that can be used in our computation:

3,723 ÷ 51

Express 3,723 as 2295 + 1428

So, we have the following representation

3,723 ÷ 51 = (2295 + 1428) ÷ 51

Expand the expression

So, we have the following representation

3,723 ÷ 51 = 2295 ÷ 51 + 1428 ÷ 51

Evaluate the quotients

3,723 ÷ 51 = 45 + 28

Next, we complete the blanks (see attachment) for the completed entries

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The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

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Answer:

144

Step-by-step explanation:

First: 6x

Second: 6x+6

Third: 6x+12

Fourth: 6x+18

- Since they're multiples of 6

\(6x+6x+6+6x+12+6x+18=540\)

\(24x+36=540\\\)

Subract 36 from each side give us...

\(24x=504\\x=21\)

\(21(6)+18=144\)

Hope this helped! Please mark brainliest :)

Answer:

b + 1.75f

Step-by-step explanation:

1.75 cups are used for every loaf of pumpkin bread.

Answer:

f(4/7)=b

Step-by-step explanation:

3+1/2=7/2

(7/2)x=2

x=4/7

the constant of the equation is 4/7

so take f and b and put f in place for 7/2 cups and b for 2 loaves of bread.

f(4/7)=b

Hope that helps :)

In this case the formula of an ellipse is

In our case a helps to the wise and b with the tall

Then if we need twice the wide

and 1.5 the tall

Therefore our new equation is

ANSWER

Answer:

r = 0.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you graph both the focus and the directrix you will see that the directrix is below the focus...12 units below to be exact. The focus is on the vertical line x = 4, so the vertex also has an x coordinate (which is actually h since h and k represent the vertex) of 4. The vertex is exactly halfway between the focus and the directrix, so that means that the vertex is at (4, 0). h = 4, k = 0. The standard form for this parabola (we know it opens upwards since the parabola ALWAYS wraps itself around the focus and is directed away from the directrix) is:

\((x-h)^2=4p(y-k)\)

p is the number of units between the focus and the vertex, or the vertex and the directrix (which is the same number of units since the vertex is smack dab in the middle of them!). That means that p = 6. Filling in 6 for p, 4 for h, and 0 for k we have:

\((x-4)^2=4(6)(y-0)\) and simplify to

\((x-4)^2=24y\) which is the first choice you're given.

The equation that shows the parabola when parabola has the focus at (4, 6) and the directrix y = –6 should be considered as the (x – 4)2 = 24y.

In terms of mathematics, a parabola represent the plane curve  in which there is the mirror-symmetrical and should be made of U-shaped.

Since there has the focus at (4, 6) and the directrix y = –6

So the first equation should be considered.

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Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

Step-by-step explanation:

In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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Answer:

0.02 or 1/50...AR n-1..... so A is the unknown

Answer:

It's A

Step-by-step explanation:

Because it's A

Answer:

A

Step-by-step explanation:

3 ∑ n=0 (-1/5)^n x 25 = 104/5

option A also = that so A

The solution of the equation -x² + 4 = x + 2 is at x = -2 and x = 1

An equation is an expression that shows how numbers and variables are related to each other.

Given the quadratic equation:

-x² + 4 = x + 2

Collecting like terms:

x² + x - 2 = 0

Plotting using a graph; the solution of the equation can be gotten by getting the point the graph crosses the x axis.

The solution is at x = -2 and x = 1

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Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

A

Step-by-step explanation:

Comment

The median of a trapezoid is the line going horizontally across the midpoint values of the 12 inch and 16 inch bases.

In other words, it is the average length of the 2 bases.

Formula

(b1 + b2 ) / 2

Solution

median Length = (16 + 12) / 2

median length = 28/2

median length = 14

Answer

median length = 14 inches

Answer:

m=-3

Step-by-step explanation:

Answer:

m= -3

Step-by-step explanation:

Answer:

8 cards

Step-by-step explanation:

Work Backwards:

30/2 is 15

15-7 is 8.

Hope this helps :D

Answer:

Step-by-step explanation:

Let x be the number of cards Jason had initially in his collection.

"Jason bought 9 new baseball trading cards to add to his collection"

x

+

9

is the equation because  

x

is the initial number of cards he has and he bought another 9

"His dog ate half of his collection"

1

2

(

x

+

9

)

because  

x

+

9

is what he had before his dog ate his cards and since his dog ate half, there is a  

1

2

added to the equation

"42 cards left"

1

2

(

x

+

9

)

=

42

Since his dog ate half, he is left with half of his initial card collection.

x

+

9

=

42

×

2

x

+

9

=

84

x

=

84

−

9

x

=

75

Answer:

Michelle finished at 8:10 pm.

Step-by-step explanation:

85 mintues can be simplified to 1hr and 25 minutes, so add 85 to 6:45 and you get 8:10 :)  If im wrong im sorry

The time at which Michelle finish her dance class is given by the equation A = 8 : 10 PM

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the time at which Michelle finished her class be A

Now , the time required for the dance class = 85 minutes

So , the time required for the dance class = 1 hour 25 minutes

The time at which Michelle started her class = 6 : 45 PM

So , the time at which Michelle finished her class A = time at which Michelle started her class + time required for the dance class

Substituting the values in the equation , we get

The time at which Michelle finished her class A = 6 : 45 PM + 1 hour 25 minutes

On simplifying the equation , we get

The time at which Michelle finished her class A = 8 : 10 PM

Hence , the equation is A = 8 : 10 PM

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The bounds of non-unusual measures are given as follows:

Hence an adult male foot length of 31.1 cm is significantly high, as it is greater than the upper bound.

The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.

Considering the mean and the standard deviation for this problem, the bounds are given as follows:

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Probability of students having their own vehicle

= 2/10

= 1/5

The amount owed in 5 years with monthly compounding, considering a $19,000 personal loan with a 15% interest rate, will be $34,558.52.

1. Convert the interest rate to a decimal: 15% = 0.15.

2. Determine the number of compounding periods: Since the loan compounds monthly, multiply the number of years by 12. In this case, 5 years * 12 months/year = 60 months.

3. Calculate the monthly interest rate: Divide the annual interest rate by 12. In this case, 0.15 / 12 = 0.0125.

4. Use the compound interest formula to calculate the future value:

  Future Value = Principal * (1 + Monthly Interest Rate)^(Number of Compounding Periods)

  Future Value = $19,000 * (1 + 0.0\(125)^{(60\))

5. Evaluate the expression inside the parentheses: (1 + 0.0\(125)^{(60\)) ≈ 1.954503.

6. Multiply the principal by the evaluated expression: $19,000 * 1.954503 = $37,133.57 (unrounded).

7. Round the final answer to the nearest cent: $34,558.52.

Therefore, in 5 years with monthly compounding, the amount owed on the $19,000 personal loan will be approximately $34,558.52.

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Answer: 8/50

Step-by-step explanation:

simplified is 4/25

Answer:

\(y=\frac{1}{3}x+7.6666\)

Step-by-step explanation:

First we must convert  \(3x+y=-7\) into slope-intercept form!

To do this we simply just need to subtract -3x from the 3x on the left and move it to the right side. This would result in: \(y = -3x-7\)

Now that we have our slope-intercept form for the equation remember that to find the equation that is perpendicular to the given equation, you need to use the opposite reciprocal of the slope. This would be \(\frac{1}{3}\) as that is the reciprocal and opposite of \(-\frac{3}{1}\)

Now in order to find the "b" variable of the equation that goes through the ordered pair (1, 8) we need to plug it in to the given equation!

That equation would be: \(y=\frac{1}{3}x-7\)

Given that x = 1 and y = 8 we can plug those in like so:

\(8=\frac{1}{3}(1)+b\)

(make sure to set the -7 to b as that's what we're solving for)

1 / 3 is 0.3333 (infinitely repeating)

Next we need to subtract 0.3333 from 8, which would be 7.6666 (infinitely repeating) Remember that the variable needs to be "alone"!

Now we have our "b" for the equation! Hence the equation would be:

\(y=\frac{1}{3}x+7.6666\)

(you can also use \(\frac{23}{3}\) for the b as that is the "exact form" of 1 / 3 but they both work)

Hope this helps! Feel free to ask questions!

(a) The general anti-gradient for ∇f(x,y) = (6x + 4y^3, –2 + 12xy^2) is f(x,y) = 3x^2 + 4xy^3 – 2y + C

(b) The general anti-gradient for ∇f(x,y) = (6x/y^2 -2e^-2x, 6x^2/y^3+4y) is f(x,y) = 3x^2/y^2 + e^-2x + 2y^2 + C

(a) To find the general anti-gradient f for ∇f(x,y) = (6x + 4y^3, –2 + 12xy^2), we need to integrate each component of the gradient with respect to its corresponding variable.

Thus, we have

f(x,y) = ∫(6x + 4y^3) dx + C1

f(x,y) = 3x^2 + 4xy^3 + C1

f(x,y) = ∫(–2 + 12xy^2) dy + C2

f(x,y) = –2y + 4x y^3 + C2

where C1 and C2 are constants of integration

Therefore, the general anti-gradient for ∇f(x,y) = (6x + 4y^3, –2 + 12xy^2) is

f(x,y) = 3x^2 + 4xy^3 – 2y + C

where C is an arbitrary constant.

(b) To find the general anti-gradient f for ∇f(x,y) = (6x/y^2 -2e^-2x, 6x^2/y^3+4y), we need to integrate each component of the gradient with respect to its corresponding variable

Thus, we have

f(x,y) = ∫(6x/y^2 -2e^-2x) dx + C1

f(x,y) = 3x^2/y^2 + e^-2x + C1

f(x,y) = ∫(6x^2/y^3+4y) dy + C2

f(x,y) = 3x^2/y^2 + 2y^2 + C2

where C1 and C2 are constants of integration.

Therefore, the general anti-gradient for ∇f(x,y) = (6x/y^2 -2e^-2x, 6x^2/y^3+4y) is

f(x,y) = 3x^2/y^2 + e^-2x + 2y^2 + C

where C is an arbitrary constant.

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The given question is incomplete, the complete question is:

Find the general anti-gradient, f, for the following: (i.e. f was the original function, and you are given the gradient of the function.) (a)  ∇f(x,y) = (6x + 4y^3, –2 + 12xy^2) (b)  ∇f(x,y) = (6x/y^2 -2e^-2x, 6x^2/y^3+4y)