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3 years ago

Susan made $117 for hours 9 of work.

1 answer:

8 0

First we need to figure out how much Susan made per hour

117/9 = 13 dollars per hour

Then find out how much she makes in 7 hours

13 • 7 = 91 dollars

$91 in 7 hours

You might be interested in

All of these ODEs model a system with a spring, mass and dashpot.

Wewaii [24]

Answer:

− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped

− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped

1 y ' ' + 7 y ' + 5 y = 0: over-damped

Step-by-step explanation:

Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:

$a_ny^n+a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

This differential equation will have a characteristic equation of the form:

$a_nr^n+a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.

If the discriminant is greater than zero, the solution is over-damped

If the discriminant is less than zero, the solution is under-damped

If the discriminant is equal to zero, the solution is critically damped

So, given the differential equation:

$-3y''-3y+3y=0$

Which has characteristic equation of the form:

$-3r^2-3r+3=0$

The quadratic polynomial of the form:

$ar^2+br+c=0$

Has discriminant:

$Disc=b^2-4ac$

In this case:

$a=-3\\b=-3\\c=3$

So:

$Disc=(-3)^2-4(-3)(3)=9-(-36)=45$

In this case:

$Disc=45>0$

Therefore the solution is over-damped.

Now, given the differential equation:

$-2y''-4y'+1y=0$

Which has characteristic equation of the form:

$-2r^2-4r+1=0$

The quadratic polynomial of the form:

$ar^2+br+c=0$

Has discriminant:

$Disc=b^2-4ac$

In this case:

$a=-2\\b=-4\\c=1$

So:

$Disc=(-4)^2-4(-2)(1)=16+8=24$

In this case:

$Disc=24>0$

Therefore the solution is over-damped.

Finally, given the differential equation:

$1y''+7y'+5y=0$

Which has characteristic equation of the form:

$1r^2+7r+5=0$

The quadratic polynomial of the form:

$ar^2+br+c=0$

Has discriminant:

$Disc=b^2-4ac$

In this case:

$a=1\\b=7\\c=5$

So:

$Disc=(7)^2-4(1)(5)=49-20=29$

In this case:

$Disc=29>0$

Therefore the solution is over-damped.

6 0

3 years ago

12-2 one step equations

Grace [21]

Answer:

N + 3 = -5

n= -8

N-4=9

n=13

4+N=10

n=6

-10+N=3

n=13

N-10=1

n=11

-11+n=-12

n=-1

N+19=20

n=1

15+N=-10

n=-25

N-6=-12

n=-6

N+4=16

n=12

Step-by-step explanation:

5 0

3 years ago

I NEED HELP NOW PLS ASAP

castortr0y [4]

Answer:

Step-by-step explanation:

hello,

I understand that there are only 4 cards and then the player draw a card out of the 4 cards, replace it so the second draw is still out of the 4 cards

How many ways can you draw two cards?

as the first card is replaced, this is 4*4=16

so there is 16 possibles ways

hearts hearts

hearts clubs

hearts diamonds

hearts spades

clubs hearts

clubs clubs

clubs diamonds

clubs spades

diamonds hearts

diamonds clubs

diamonds diamonds

diamonds spades

spades hearts

spades clubs

spades diamonds

spades spades

out of these 16 ways, how many have same colour for both cards?

I assume that there are only two colours Red and Black, so we can have

only 8 ways so the first probability is 8/16 = 1/2

out of these 16 ways, how many are red ace first and black ace?

There are 4 ways so the probability is 4/16 = 1/4

hope this helps

8 0

3 years ago

Read 2 more answers

How are numerical expressions and algebraic expressions different

lozanna [386]

Numerical expressions use numbers and algebraic expressions use variables.

7 0

3 years ago

A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates

postnew [5]

Answer

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as $y=mx+c$ where $m$ is the slope and $c$ is the intercept on the $y$ -axis. The slope describes how $y$ changes when $x$ changes. A negative value means the it is a decreasing change. In our case, $y$ is $A$ and $x$ is $t$ . Thus, the slope of the equation is $m=-0.062$ . This means that the area of glacier is decreasing by $0.062 \text{km}{}^2 = 62000 \text{m}{}^2$ every year since 2000.

b) The $A$ -intercept (= 16.2 $\text{km}{}^2$ ) represents the area covered when $t=0$ . But $t=0$ starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 $\text{km}{}^2$ .

c) $A=f(t)$ means the area covered after year 2000. Setting it to 12 means the area covered after $t$ years is 12 $\text{km}{}^2$ ). $t$ is therefore the number of years since 2000 that the total area covered will be 12 $\text{km}{}^2$ ).

d) $f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2$ to 1 decimal place.

e) The term involving $t$ represents the disappearing area. In 12 years, the disappeared area is $0.062\times12=0.744 =0.7 \text{km}{}^2$ to 1 decimal place.

f) $f(t)=16.2−0.062t =12$

$0.062t = 16.2-12 = 4.2$

$t = \dfrac{4.2}{0.062}=67.7419\ldots =67.7$ years to 1 decimal place.

8 0

3 years ago