find last years salary if, after a 6% pay raise, this years salary is $33,920​

Answer:

4x+10

Step-by-step explanation:

Emma is guaranteed to use 10 pages when she writes something. Since you can't tell how many hours she has written, you use x to represent the hours she has spent writing. If she writes 4 pages every hour, that would be 4 × (hours spent writing) or 4x. Add 4x to the original guaranteed 10 pages she uses and you have your expression.

Answer:

2(24+9x)

Step-by-step explanation:

Answer:

6(8+3x)

Step-by-step explanation:

48+18x=6(8+3x)

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

on edge

47 miles taxi ride will cost $32.9

Step-by-step explanation:

Given,

Cost every 36 miles = $25.20

Cost of one mile = [tex]\frac{Cost\ for\ 36\ miles}{36}[/tex]

Cost of one mile = [tex]\frac{25.20}{36}\\[/tex]

Cost of one mile = $0.7

Cost of 47 miles = Cost of one mile * 47

[tex]Cost\ of\ 47\ miles = 0.7*47\\Cost\ of\ 47\ miles = \$32.9[/tex]

47 miles taxi ride will cost $32.9

Keywords: Division, multiplication

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Answer:

9.694 years

Step-by-step explanation:

Let the investment is $P.

So, we are asked to determine the time it will grow to triple with the compound interest rate of 12%.

Let the time is y years.

So, from the formula of compound interest we can write

[tex]3P = P(1 + \frac{12}{100} )^{y}[/tex]

⇒ [tex](1 + \frac{12}{100} )^{y} = 3[/tex]

⇒ [tex](1.12)^{y} = 3[/tex]

Now, taking log both sides we get,

y log 1.12 = log 3 {Since, [tex]\log a^{b} = b \log a[/tex] }

⇒ 0.04922y = 0.477712

⇒ y = 9.694 years (Answer)

Answer:

The correct answer is A. Approximately 10.4 kg.

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Weight of the astronaut on Earth = 49 kg

Weight of the astronaut on the moon = 1/6 * 49 kg

Weight of the astronaut on Mars = 0.38 * 49 kg

2. What is the  difference between the astronaut's weight on Mars and her  weight on the moon? Round your answer to the nearest  tenth.

Weight of the astronaut on the moon = 1/6 * 49 kg

Weight of the astronaut on the moon = 8.2 kg

Weight of the astronaut on Mars = 0.38 * 49 kg

Weight of the astronaut on Mars = 18.6 kg

Difference between the astronaut's weight on Mars and her  weight on the moon = 18.6 - 8.2

Difference between the astronaut's weight on Mars and her  weight on the moon = 10.4 kg

Answer:

Infinitely many solutions.

Step-by-step explanation:

3x-5y=15

6x-10y=30

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

simplify 6x-10y=30 into 3x-5y=15

Answer:

C, Since there is is more then one solution

Step-by-step explanation:

Answer:

So a ratio of 8:3 means for every 8 cars that is 3 trucks so we have the number of trucks which is 21 so what i did to find the answer was see how many times 3 went into 21 which is 7 times then you would take the 7 and times it by 8 and get 56 so there are 56 cars.

Step-by-step explanation:

Final answer:

To determine the number of cars, we use the ratio of cars to trucks (8 to 3) with the total number of trucks (21) to find the common multiplier. Multiplying the ratio number for cars (8) by the multiplier (7) gives us 56 cars in the parking lot.

Explanation:

Calculating the Number of Cars in a Parking Lot

To calculate the number of cars in the parking lot when we know the ratio of cars to trucks and the number of trucks, we can set up a proportion. Given that the ratio of cars to trucks is 8 to 3 and there are 21 trucks, we can represent the number of cars as 8x and the number of trucks as 3x, where x is the common multiplier for the ratio. Since we know there are 21 trucks, we can set 3x equal to 21 and solve for x:

3x = 21

Divide both sides of the equation by 3:

x = 21 / 3

x = 7

Now that we have the value of x, we can find the number of cars by multiplying the ratio number for cars (8) by x (7):

Number of cars = 8 x 7

Number of cars = 56

Therefore, there are 56 cars in the parking lot.

You can solve the kinetic energy formula E = mv² for 'v' by first dividing by 'm' to get E/m = v² and then taking the square root of both sides, resulting in v = sqrt(E/m).

The kinetic energy of an object is given by the equation E = mv², where 'm' is the mass of the object and 'v' is its speed. If you want to solve this formula for 'v', you would start by dividing both sides of the equation by 'm'. Doing this, you would get: E/m = v². Then, you would take the square root of both sides to isolate 'v'. This would give you: v = sqrt(E/m), where sqrt stands for 'square root'.

This means that the speed of the object can be found by taking the square root of the kinetic energy divided by the mass of the object.

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The expression for y is y = [tex]\frac{2E}{m}[/tex].

To solve the kinetic energy formula E=[tex]\frac{1}{2}[/tex] [tex]mv^{2}[/tex] for y, we need to isolate y on one side of the equation. The formula can be rearranged as follows:

E=[tex]\frac{1}{2}[/tex][tex]mv^{2}[/tex]

Multiply both sides of the equation by 2 to eliminate the fraction:

2 E =  [tex]mv^{2}[/tex]

Now, to solve for y, which is represented by [tex]mv^{2}[/tex] , divide both sides by m:

y = [tex]\frac{2E}{m}[/tex]

So, the expression for y is y =  [tex]\frac{2E}{m}[/tex] .

This final equation tells us that y (representing [tex]mv^{2}[/tex] ) is equal to twice the kinetic energy (E) divided by the mass (m) of the object.

In physics, [tex]mv^{2}[/tex] is often associated with momentum or the force needed to change the object's velocity.

This derived formula provides a clear representation of the relationship between kinetic energy, mass, and velocity in terms of y.

Question

The formula for finding the kinetic energy, E, of an object is given below, where m represents the mass and v represents the speed of the object. E= 1/2 mv^2 Solve the formula for y.

Answer: Equation for total cost: T = $25 + 0.04E

Cost of a client who earns $1500 = $85

Step-by-step explanation:

Let E = earning in the first month

Commission (c) = 0.04 (4%) × E

Total cost will be the addition of $25 fixed amount and commission

Therefore, an equation that will represent total cost of finding a job through the hotline will be:

T = $25 + 0.04E

The cost of a client whose first month earnings is $1500 will be

T = $25 + 0.04 ($1500)

T = $25 + $60 = $85

I found that helpful

Answer:

1,495,672

Step-by-step explanation:

Build a table to track the number of adult rats, 3-week old rats (let's call them teens), and baby rats.

[tex]\left[\begin{array}{ccccc}Week&Adult&Teen&Baby\\1&2&0&0\\3&2&0&10\\6&2&10&10\\9&12&10&10\\12&22&10&60\\15&32&60&110\\18&92&110&160\end{array}\right][/tex]

The pattern is this: every 3 weeks, the number of adults becomes the previous number of adults + the number of teens.  The number of teens becomes the previous number of babies.  And the number of babies becomes the previous number of adults × 5.

Continuing:

[tex]\left[\begin{array}{ccccc}Week&Adult&Teen&Baby\\1&2&0&0\\3&2&0&10\\6&2&10&10\\9&12&10&10\\12&22&10&60\\15&32&60&110\\18&92&110&160\\21&202&160&460\\24&362&460&1010\\27&822&1010&1810\\30&1832&1810&4110\\33&3642&4110&9160\\36&7752&9160&18210\\39&16912&18210&38760\\42&35122&38760&84560\\45&73882&84560&175610\\48&158442&175610&369410\\51&334052&369410&792210\end{array}\right][/tex]

So at the end of the year, there are a total of 1,495,672 rats.

Answer:

39

Step-by-step explanation:

product = 2 numbers multiplied by each other

8 x 4 = 32

32 + 7 = 39

The product of two numbers is when you multiply those two numbers together.

So, the product of 8 and 4 would simply be 8 * 4=32

7 more than 32 would simply be 32 + 7=39

The answer is 39

Answer:

2x + y + 5 = 0

Step-by-step explanation:

y − 1 = -2 (x + 3)

y − 1 = -2x − 6

2x + y + 5 = 0

Answer:

410:1

Step-by-step explanation:

Answer:

h=87/3

Step-by-step explanation:

3=87/h

h=87/3

Answer:

Step 1) is incorrect.

Step-by-step explanation:

Answer:

Step one is the one that is wrong

Step-by-step explanation:

Cat hacker

Answer:

20%

Step-by-step explanation:

1.92 - 1.60 = 0.32

percentage increase = (0.32/1.60) * 100 =

0.2 * 100 = 20%

Answer: required percent increase in price=20%

Step-by-step explanation:

required percent increase in price=[tex]\frac{1.92-1.60}{1.60}[/tex]\times100

                                                       =[tex]\frac{0.32}{1.60}[/tex]\times100

                                                       =[tex]0.20\times100[/tex]

                                                      =20%

Answer:

In this exercise we have to solve the following inequality:

[tex]6h-18<6h+1[/tex]

Step 1. Subtract 6h from both sides:

[tex]6h-18-6h<6h+1-6h[/tex]

Step 2. Simplify:

[tex]6h-6h-18<6h-6h+1 \\ \\ -18<1[/tex]

This is always true because -18 is a number less than 1. Therefore, for any real h-value the inequality is always true.

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Answer:

93750 L

Step-by-step explanation:

P1V1 = P2V2

1.2 atm*125000L = 1.6 atm* V2

V2 = 93750 L

The new volume of the gas is 93750 liters.

Given,

The volume of gas in a container is 125,000 liters.

The pressure is 1.2 atmospheres.

Suppose the temperature remains constant.

The pressure changes to 1.6 atmospheres.

We have to find the new volume of the gas.

The equation is given by:
PV = nRT

Where P is the pressure of the gas.

V is its volume.

n is the number of moles of the gas.

T is its kelvin temperature.

R is the ideal (universal) gas constant.

Let the initial volume and pressure of the gas be [tex]V_{1}[/tex] and [tex]P_{1}[/tex].

The final volume and pressure of the gas be [tex]V_{2}[/tex] and [tex]P_{2}[/tex].

We have,

[tex]V_{1}[/tex] = 125000 litres.

[tex]P_{1}[/tex] = 1.2 atmospheres.

Since temperature remains constant.

[tex]P_{1} V_{1}[/tex] / nR = T and [tex]P_{2} V_{2}[/tex] / nR = T

We can write as:

[tex]P_{1} V_{1}[/tex] / nR = [tex]P_{2} V_{2}[/tex] / nR

[tex]P_{1} V_{1}[/tex]  = [tex]P_{2} V_{2}[/tex]

Putting the values we get,

[tex]P_{1} V_{1}[/tex]  = [tex]P_{2} V_{2}[/tex]

1.2 x 125000 = 1.6 x [tex]V_{2}[/tex]

[tex]V_{2}[/tex] = (1.2 x 125000) / 1.6

   = 93750 litres.

Thus the new volume of the gas is 93750 liters.

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Answer:

[tex]\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)} are\ in\ AP[/tex]

Step-by-step explanation:

Given that [tex](b-c)^2, (c-a)^2 , (a-b)^2[/tex] are in AP

To prove: [tex]\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)}[/tex] are in AP

From given as we know if p , q, r are in AP then 2q= p+r.

[tex]2(c-a)^2= (b-c)^2+(a-b)^2\\\\\Rightarrow 2(c^2+a^2-2ac)=b^2+c^2-2bc+a^2+b^2-2ab\\\\\Rightarrow 2c^2+2a^2-4ac= 2b^2+c^2+a^2 -2bc-2ab\\\\\Rightarrow a^2+c^2-2b^2-4ac= -2bc-2ab\\\\\Rightarrow a^2-2b^2+c^2= 4ac-2bc-2ab[/tex]

Now

[tex]\dfrac{1}{(b-c)},\dfrac{1}{(c-a)} ,\dfrac{1}{(a-b)}2\dfrac{1}{(c-a)} =\dfrac{1}{(b-c)}+\dfrac{1}{(a-b)}\\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-b+b-c}{(b-c)(a-b)} \\\\\Rightarrow \dfrac{2}{(c-a)}= \dfrac{a-c}{(b-c)(a-b)} \\\\\Rightarrow2(b-c)(a-b) = (c-a)(a-c) \\\\\Rightarrow 2(ab-b^2-ac+bc)= -(a-c)^2\\\\\Rightarrow 2ab- 2b^2-2ac+2bc = -a^2-c^2+2ac\\\\\Rightarrow a^2-2b^2+c^2=4ac-2ab-2bc[/tex]

Which is the result of AP

.

Hence proved

Answer: 7

Step-by-step explanation:

35 x 0.20 = 7

Answer:3x+18

Step-by-step explanation:

Answer:

y = x + 2

Step-by-step explanation:

4x - 4y = -8 can be rearranged to slope-intercept form by isolating y.

[tex]4x - 4y = -8\\-4y = -8 - 4x\\y =\frac{-8-4x}{-4} \\y = 2 + x\\y = x + 2[/tex]

Answer:

The offer of 30% off a single item of $ 1000 or more will save most money on these appliances .

Step-by-step explanation:

Given as :

The purchase price = $ 2000

The offering discount = 15 %

Let The price of item after discount = x

So , x = ( $ 2000 ) - ( $ 2000 × 15 % )

Or,  x = ( $ 2000 ) - ( $ 2000 × 0.15 )

Or,  x = ( $ 2000 ) - ( $ 300 )

∴     x =  $ 1700

Now, Again

The purchase price = $ 1000

The offering discount = 30 %

Let The price of item after discount = y

So , y = ( $ 1000 ) - ( $ 1000 × 30 % )

Or,  y = ( $ 1000 ) - ( $ 1000 × 0.3 )

Or,  y = ( $ 1000 ) - ( $ 300 )

∴     y =  $ 700

Now, If we purchase two item at the cost price of $ 700 each , then it will cost as $ 700 × 2 = $ 1400

And for the same number of items at the cost price is $ 1700 after 15 % discount on list price of $ 2000 , So the second offer will save most .

Hence The offer of 30% off a single item of $ 1000 or more will save most money on these appliances . Answer

Answer:

The Domain D = {y ∈ R / y ≠ [tex]\dfrac{b}{2}[/tex] y ≠ 0}

Step-by-step explanation:

Let ,

f(y) = [tex]\dfrac{b^{2} - 4by }{2y^{2} - by }[/tex] - [tex]\dfrac{4y}{b-2y}[/tex]

The above function would be defined only when the denominator of anyone or both the terms of the function do not become 0 -

[tex]2y^{2} - by[/tex] ≠ 0 and b - 2y ≠ 0

∴ y(2y - b) ≠ 0                 and y ≠[tex]\dfrac{b}{2}[/tex]

Either y ≠ 0 or y ≠ [tex]\dfrac{b}{2}[/tex]

∵ The domain of a function consists of only those points where the function is defined -

The Domain D consists of all y ∈ Real numbers such that y ≠ 0 and y ≠ [tex]\dfrac{b}{2}[/tex]

a. An equation that represents the situation is y = 9 x

b. The best Interpretation of the slope is " It costs $9 per hour to rent a kayak " ⇒ 2nd answer

c. It costs $45 to rent the kayak for 5 hours

Step-by-step explanation:

Proportional relationship means two quantities vary with each other

If y varies directly as x, then

The cost " y " in (dollars) to rent a kayak is proportional to the

number of hours  " x " that you rent the kayak

∵  y ∝ x

∴ y = k x , where k is the constant of proportionality

∵ It costs $27 to rent the kayak for 3 hours

∴ y = 27 and x = 3

- Substitute these value in the equation above

∴ 27 = k (3)

- Divide both sides by 3

∴ 9 = k

∴ y = 9 x

a. An equation that represents the situation is y = 9 x

∵ The slope is the unit rate of the cost

∵ The slope = 9

∴ The unit rate is $9 per hour

b. The best Interpretation of the slope is " It costs $9 per hour to rent a kayak "

∵ y = 9 x

∵ x = 5 hours

- Substitute x by 5 in the equation above

∴ y = 9 (5) = $45

c. It costs $45 to rent the kayak for 5 hours

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Final answer:

The equation representing the situation is y = 9x. The slope indicates that it costs $9 per hour to rent the kayak. For 5 hours of rental, the cost is $45.

Explanation:

If the cost (y) to rent a kayak is proportional to the number (x) of hours the kayak is rented, and it costs $27 to rent the kayak for 3 hours, we can use this information to write a linear equation that represents the situation. The cost is $9 per hour since $27 ÷ 3 hours = $9 per hour. Our equation is thus y = 9x.

For the interpretation of the slope, since we've determined the cost is $9 per hour, the correct interpretation of the slope is that it costs $9 per hour to rent the kayak.

To find out how much it costs to rent the kayak for 5 hours, we simply plug in x = 5 into our equation y = 9x. So, it costs y = 9 × 5 = $45 to rent the kayak for 5 hours.

Answer:

nothing has changed about the shape

Step-by-step explanation:

the shapes perimeter has neither grown or shrunk as it wasn't dialated only moved

Answer:

x=3y/4 - 7/4

Step-by-step explanation:

Answer:

x = [tex]\frac{3y-7}{4}[/tex]

Step-by-step explanation:

Given

7 + 4x = 3y ( subtract 7 from both sides )

4x = 3y - 7 ( divide both sides by 4 )

x = [tex]\frac{3y-7}{4}[/tex]

Answer:

10 face cards and 5 non-face cards

Step-by-step explanation:

If x is the number of face cards, and y is the number of non-face cards, then:

x + y = 15

10x + 5y = 125

Solve the system of equations.  Using substitution:

10x + 5 (15 − x) = 125

10x + 75 − 5x = 125

5x = 50

x = 10

y = 15 − x

y = 5

He drew 10 face cards and 5 non-face cards.

The best way that Leroux can reduce the costs of regular health care without driving up the price of their health care plan is this: c. Reduce the co-pay amounts but increase the annual deductible so that the monthly premium can stay the same.

The best way that Leroux can reduce the costs of regular health care without increasing the price of the plan would be for then to reduce the co-pay amounts and then increase the annual deductible.

Annual deductibles are the amounts that the customers are expected to pay themselves while the premium is covered by the health company.

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