Candice works at a grocery store. She works 35 hours a week and
gets paid $8.50 an hour. For every hour over 35, Candice gets
paid $10 an hour. If she was paid $357.50 last week, how many
hours over 35 did Candice work?

Answer:

Step-by-step explanation:

From the information given:

Tank's Capacity = 600 gal

Original content of water = 200 gal

Salt solution = 100 lb

In the tank:

Suppose x(t) = amount of salt at time (t); &

V(t) = volume of water

Then,

V(t) = 200 + t

and [tex]x'(t) = 3 - \dfrac{2x(t)}{200+t}[/tex]

From the above linear equation, the integrating factor can be computed as:

[tex]x(t) = \Bigg(e^{\int \dfrac{2}{200+t}} \Bigg)^{dt}[/tex]

[tex]= e^{2 \ log (200+t)}[/tex]

= (200 + t)²

The general solution can now be expressed as:

[tex]x(t) = \dfrac{1}{(200+t)^2}\Bigg( \int 3(200+t)^2 \ dt +C\Bigg)[/tex]

We know that C = integrating factor, thus taking the integral:

[tex]x(t) = \dfrac{(200+t)^3 +C}{(200+t)^2}[/tex]

At the initial condition, x(0) = 100

∴

[tex]100= \dfrac{(200)^3 +C}{(200)^2}[/tex]

C = ((200)²×100) - 200³

C = -4 × 10⁶

Hence, at any time t, the amount of salt is:

[tex]x(t) = \dfrac{(200+t^2) - 4\times 10^6}{(200+t)^2}[/tex]

Answer:

She wrongly added the equations

Step-by-step explanation:

Given

[tex]-3x + y = 8[/tex]

[tex]-3x + y = -4[/tex]

Required

Her mistake

The mistake is when she added the equations.

When both equations are added, the result is:

[tex]-3x -3x + y+y=8-4[/tex]

[tex]-6x +2y=4[/tex]

and not

[tex]2y = 4[/tex]

The suggestion to avoid such mistake is for the student to check the appropriate signs of each term before adding/subtracting.

Answer:

-2i - 3

I can't see a simpler way to explain it. You just have to work your way through each step.

Step-by-step explanation:

The question is what is i^303?

Remember that when the power is divisible by 4 the expression changes to 1

i^1 = i

i^2 = i * i = sqrt(-1)*sqrt(-1) = - 1

i^3 = i^2 * i = - i

i^4 = i^2 * i^2 = -1 * - 1 = 1

So what does i^303 =

i^300 * i^3

But 300 is evenly divisible by 4. (300 / 4 = 75) so i^300 = 1^75

i^3 = -i

So now you are ready to do the question

(2 - 3i) * -i

2*-i - 3i(-i)

-2i - 3(i^2 * - 1)

-2i - 3(-1 * - 1)

-2i - 3(1)

-2i - 3

Answer:

okay, we need to add up for all k=1 till k=22

we could do it like this

(-4*1 -13) + (-4*2 -13) + (-4*3 -13) + ...

but this is long and boring, so we need another valid, yet vastly faster method to calculate this sum

we know that the "-13" part will occur 22 times, so let's write this component as "-13*22"

the -4k gents bigger with each step, k will take all the natural numbers from 1 to 22

so we could write

"-4 * (1+2+3+4+5+6+7...+21+22l

alot simpler and faster, but not fast enough

let's add up all numbers from 1 to 22 into one number

1 + 22 = 23

2 + 21 = 23

3 + 20 = 23

...

this works eleven times (bc we use up 2 numbers in each step), so the numbers from 1 to 22 added up are just

23*11= 230+23 = 252

now let's construct the final calculation

-4 * 252 -13*22 = -1294

there's your sum.

hope it helps you overall.

brainliest would be very kind ic some else leaves an answer, may it be just a greeting

Answer:

31 and a half

Step-by-step explanation:

not sure tho_____________

Answer:

31.5 is ur answer

Step-by-step explanation:

so what you have to do is add up 5.5 + 5.5 + 6+ 7 +7.5 which gives u 31.5

Answer:

.101501615

.84982392

.901244701

Step-by-step explanation:

For this question use a binomial distribtuion

a.

12C3*.44³*(1-.44)⁹= .101501615

b.

to find at least 4 find the probability of less than 4 and take its compliment

12C0*(1-.44)¹²+12C1*.44*(1-.44)¹¹+12C2*.44²*(1-.44)¹⁰+12C3*.44³*(1-.44)⁹= .15017608

1-.15017608=.84982392

c.

To find less than eight's probability find the proability of at least 8 and take its compliment

12C8*.44⁸(1-.44)⁴+12C9*.44⁹(1-.44)³+12C10*.44¹⁰(1-.44)²+12C11*.44¹¹*(1-.44)+12C12*.44¹²= .098755299

1-.098755299= .901244701

Answer:

3x-26=2x(because they are vertical angle)

or,3x-2x=26

therefore x=26

Answer:

Step-by-step explanation:

2x + (3x-26) = 90

5x = 90+26

5x = 116

x = 116/5

x = 23.2

Answer:

Her grant in four years time will be of $13108.

Step-by-step explanation:

Exponential equation:

An exponential equation has the following format:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the initial value and r is the growth rate, as a decimal.

A student get a grant of $10000 a year assuming her grant is increased by 7% each year

This means that [tex]A(0) = 10000, r = 0.07[/tex]

So

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 10000(1+0.07)^t[/tex]

[tex]A(t) = 10000(1.07)^t[/tex]

What will her grant be in four years time?

This is A(4). So

[tex]A(t) = 10000(1.07)^t[/tex]

[tex]A(4) = 10000(1.07)^4 = 13108[/tex]

Her grant in four years time will be of $13108.

Answer:

The answer is 5184. Hope it helps luv

Answer:

9

Step-by-step explanation:

3 - ( -6 ) = 9

Hope this helps! Brainliest?

Answer:

9

Step-by-step explanation:

the other answer is right.

to add a little bit of explanation :

you need to calculate the difference between -6 and +3.

and we are looking on the number line only for a distance and not for a direction, as the distance (or simple difference) between -6 and +3 is the same as between +3 and -6.

so, whatever we get as difference, we need to treat that result as positive number.

so, we get the difference between two numbers by subtracting one from the other.

either 3 - (-6), or -6 - 3

you do know that subtracting a negative number is the same as adding the same positive number ?

e.g. 3 - (-6) = 3 + 6 = 9

as for the other direction -6 - 3 = -9

but again, we have to take this in this context as a positive number.

in math we call this the absolute value of a number.

so, the answer is always 9.

Answer:

There are 54 in total because if you add them all it gets you 54

Answer:

Step-by-step explanation:

Answer:

[tex]6n \div 4[/tex]

Step-by-step explanation:

n is a variable and multiplied by 6, so it is attached to 6. (6 is known as the coefficient.) Then it is divided by 4. (4 is known as the constant because there is no variable attached to it.)

[tex]6n \div 4[/tex]

Answer:

1539.4

Step-by-step explanation:

Steps:

Volume of a cylinder= πr²h

radius= diameter/2

         = 14/2

         = 7 cm

Volume= π x 7² x 10

            = 1539.38

            = 1539.4 cm³

Answer:

1539.4

Step-by-step explanation:

to find the area of a cylinder, you solve pi x radius²

3.14 x 7² = 153.94

then you multiply times the height

153.94 x 10 = 1549.4

Answer:

1. 2 is the correct answer

Step-by-step explanation:

24+67-67+78 = 102

102 /2+6-89-4​

= 1. 2

I am sure about my answer , trust me.

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

A. -8

B. 23

C. 3

D. 5

Step-by-step explanation:

Answer:

-3 1/2 or -3.5

Step-by-step explanation:

* means multiply

just put 3 where the x is

so

f(x) = -2 ( 1 - 1/4 x )

f( -3) = -2 ( 1 - 1/4 * -3 )

f( -3) = -2 ( 1 3/4 )

f( -3) = - 3 1/2

Answer:

the answer would be b I'm pretty sure

Answer:

5.5 hours

Step-by-step explanation:

Since every house has an initial charge of $50, we can begin with that

($50)

Then, let's define h as the number of hours. We know every hour is $70, although the hours is yet unknown so that can be

($70 * h) or simply ($70h)

Now, we know the total should end up to be $435, so after PEMDAS the equation will be

($70h + $50 = $435).

We subtract 50 from both sides so now we have $70h = $385.

Now we divide both sides by 70, giving us h = 5.5. Hope it helped!

The number of hours that the plumber work on the house calls should be 5.5.

Given that,

Based on the above information, the equation is as follows:

70h + 50 = 435

70h = 385

h = 5.5 hours

Therefore we can conclude that the number of hours that the plumber work on the house calls should be 5.5.

Learn more: brainly.com/question/3530056

Answer:

80

Step-by-step explanation:

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Jessica left her running shoes at school yesterday. Today she walked 4 miles to school to get her shoes, she ran home along the same route, and the total time for both trips was 2 hours. Jessica walked and ran at constant speeds, and she ran 3 miles per hour faster than she walked.

What was Jessica's walking speed in miles per hour?

Answer:

In the problem, the value of x is equal to 6a.

Step-by-step explanation:

For this equation, we are to solve for x.  

11ax + 12ax = 13ax + 60

Add together 11 and 12 because they have like terms.

23ax = 13ax + 60

Substract 13ax on both sides.

10ax = 60

Now, we divide by 10 on both sides.

ax = 6

In order to see what x is, divide a on both sides.

x = 6a

Answer:

60.8 mm^2

D

Step-by-step explanation:

Remark

You have to assume that the left and right sides are both 9.3. The question is undoable without that assumption.

Next, you have to assume that The top is 7.8 mm across and both ends meet 9.3 at right angles. Again if that is not true, the problem can't be done. Sometimes people making these questions make errors which you are asked to correct.

Solution

So let's assume that everything I've assumed is correct.

Find the area of the rectangle.

Area = L*W

L = 9.3

W = 7.8

Area = 7.8 * 9.3

Area = 72.54        Do your rounding at the end.

Now find the are of the triangle that has been cut out.

The height = 3

The base = 7.8

Area = 1/2 b * h

Area = 1/2 7.8 * 3

Area = 11.7

The area of the figure = area of the rectangle - the triangle's area

Figure Area = 72.54 - 11.7

Figure Area = 60.84

Given:

The function is:

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

The graphs of functions [tex]f(x)[/tex] and [tex]g(x)[/tex].

To find:

The function [tex]g(x)[/tex].

Solution:

We have,

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

The function [tex]f(x)[/tex] is vertically compresses to get the graph of the function [tex]g(x)[/tex]. So, the function [tex]g(x)[/tex] is:

[tex]g(x)=kf(x)[/tex]

[tex]g(x)=kx^2[/tex]               ...(i)

From the given graph it is clear that the graph of the function [tex]g(x)[/tex] passes through the point (3,3). So, putting [tex]x=3[/tex] and [tex]g(x)=3[/tex] in the above function, we get

[tex]3=k(3)^2[/tex]

[tex]3=9k[/tex]

[tex]\dfrac{3}{9}=k[/tex]

[tex]\dfrac{1}{3}=k[/tex]

Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get

[tex]g(x)=\dfrac{1}{3}x^2[/tex]

Therefore, the correct option is D.

Answer:

$4800

Step-by-step explanation:

SI=PRT DIVIDED BY 100..

So it is going to be 400×2×6 divided by 100 which will be 4800

Answer:

A-10

B- -12

C-3.6

If you cant understand B is -12