A school raised $4,000 for its new library. 36% of the money is used to buy reference book. How much money is used to buy reference books?

Answer:

193 gallons

Step-by-step explanation:

Given

[tex]A(t) = 30+8t-\frac{2}{3}(t+1)^{\frac{3}{2}}[/tex]

Required

Determine the maximum amount of water the tank can hold --- Missing from the question

Start by differentiating A w.r.t t

[tex]A'(t) = 0 + 8 + \frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}}][/tex]

Solving: [tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}}[/tex]

[tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}} = -\frac{2}{3}\frac{d}{dt}[(t+1)^{\frac{3}{2}}[/tex]

Apply power rule:

[tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}} = -\frac{2}{3}[\frac{3}{2}(t + 1)^{\frac{3}{2}-1} * \frac{d}{dt}[t+1][/tex]

[tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}} = -(t + 1)^{\frac{3}{2}-1} * \frac{d}{dt}[t+1][/tex]

[tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}} = -(t + 1)^{\frac{3}{2}-1} * [1+0][/tex]

[tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}} = -(t + 1)^{\frac{3}{2}-1} * [1][/tex]

[tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}} = -(t + 1)^{\frac{3}{2}-1}[/tex]

[tex]\frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}} = -(t + 1)^{\frac{1}{2}}[/tex]

So:

[tex]A'(t) = 0 + 8 + \frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}}][/tex]

A'(t) = 0 + 8 + \frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}}]

[tex]A'(t) = 0 +8 -(t + 1)^{\frac{1}{2}}[/tex]

[tex]A'(t) = 8 -(t + 1)^{\frac{1}{2}}[/tex]

Equate to 0 to solve for t

[tex]A'(t) = 0[/tex]

[tex]8 -(t + 1)^{\frac{1}{2}} = 0[/tex]

Collect Like Term

[tex]-(t + 1)^{\frac{1}{2}} = -8[/tex]

Square both sides

[tex](-(t + 1)^{\frac{1}{2}})^2 = (-8)^2[/tex]

[tex]t +1 = 64[/tex]

Make t the subject:

[tex]t = 64 - 1[/tex]

[tex]t = 63[/tex]

So, the tank is at maximum when t = 63.

Substitute 63 for t in: [tex]A(t) = 30+8t-\frac{2}{3}(t+1)^{\frac{3}{2}}[/tex]

[tex]A(63) = 30+8*63-\frac{2}{3}(63+1)^{\frac{3}{2}}[/tex]

[tex]A(63) = 30+8*63-\frac{2}{3}(64)^{\frac{3}{2}}[/tex]

[tex]A(63) = 30+8*63-\frac{2}{3}*512}[/tex]

[tex]A(63) = 30+8*63-\frac{2*512}{3}}[/tex]

[tex]A(63) = 30+8*63-\frac{1024}{3}}[/tex]

[tex]A(63) = 30+8*63-341.33[/tex]

[tex]A(63) = 192.67[/tex]

Approximate:

[tex]A(63) = 193[/tex]

Answer:

A= (6,76.5)

B =(32,18)

C=(80,0)

Step-by-step explanation:

The inequalities given are ;

3x + 8y ≥ 240

9x + 4y ≥ 360

x≥6

y≥0

The graph for the inequalities is as follows;

From the graph,

A= (6,76.5)

B =(32,18)

C=(80,0)

Answer:

300g butter, 1518g caster sugar, 3518g plain flour, 100g cornflour

Step-by-step explanation:

servings show are for 8, times everything by 2 to get 16 servings :)

Answer:

i really  really like ya cut g

Step-by-step explanation:

Answer:

Sorry but I dont  know.

Step-by-step explanation:

Answer:

B. $352.80

Step-by-step explanation:

edge 2021

The principal on the loan with interest rate of 6% is $2000.

Given that a loan is given in the interest rate of 6%, interest received is $840 and the duration of the loan is 7 years,

We need to find the principal on the loan,

To find the principal on the loan, we can use the formula for simple interest:

Interest = Principal × Rate × Time

In this case, we know the interest is $840.00, the rate is 6%, and the time is 7 years.

Let's solve for the principal:

Principal = Interest / (Rate × Time)

Principal = $840.00 / (0.06 × 7)

Principal ≈ $840.00 / 0.42

Principal ≈ $2000.00

Therefore, the principal on the loan is $2000.00.

Learn more about simple interest click;

https://brainly.com/question/30964674

#SPJ4

Answer:

So if you are in middle school like me, they are asking for an equation answer, and that equation is 4 divided by 2/5 = _ and _ x 2/5 = 4

Step-by-step explanation:

Answer:

$25,500

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year,

then, solving our equation

I = 15000 × 0.07 × 10 = 10500

I = $ 10,500.00

The simple interest accumulated

on a principal of $ 15,000.00

at a rate of 7% per year

for 10 years is $ 10,500.00.

Answer:

24 feet

Step-by-step explanation:

Given that,

Mrs. Booker had to run 8 yards to make it to a safe zone.

We need to convert this distance in feet.

The conversion from yards to feet is as follows :

1 yard = 3 feet

So,

8 yards = 24 feet

Hence, Mrs. Booker had to run 24 feet to make it to a safe zone.

Answer:33

Step-by-step explanation:

Answer:

you checked the right box. Its b

Step-by-step explanation:

22/5 divided by 2/5 is 11

b

Answer:

Is 6x and 4x+2 equivalent

? No!

Step-by-step explanation:

6x doesn't equal 4x+2

In order for them to be the same you would have to add the same terms example:

4x+2x would equal 6x

Extra explaining:

The only way for those term to be added would be if they had the same variable since only 4x has a variable the 2 cant be added. In math you CANNOT move your variables off of a number and add them back on after.

Answer:

58x i think. i hope thiss helps

Answer:

31x

Step-by-step explanation:

x * 5 = 5x

3x * 12 = 36x

36x - 5x = 31x

first you have to find the area of the big rectangle and the little rectangle too and then subtract the area of the big rectangle to the little rectangle to find the area of the Shaded region

Answer:

p = 2

Step-by-step explanation:

[tex]\frac{p}{18}[/tex] = [tex]\frac{8}{72}[/tex]

to work with smaller numbers you can look to reduce

for example, 8/72 can be reduced to 1/9

[tex]\frac{p}{18}[/tex] = [tex]\frac{1}{9}[/tex]

now you can cross-multiply:

9p = 18

p = 18/9 which is 2

Answer:

24

Step-by-step explanation:

Answer:

It is 35

Step-by-step explanation:

34+1=35

Happy to help

Answer:

[tex] - 2 {x}^{2} - 8x - 5[/tex]

hope it's helpful ❤❤❤❤❤❤

THANK YOU.

#

Answer:

x = 30

Step-by-step explanation:

AB  is a tangent to the circle so ∠ ABO = 90°

The sum of the 3 angles in a triangle = 180° , then

x + 2x + 90 = 180

3x + 90 = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer: x = 30

OA cuts the circle (O) at C

because ∠ABC is the  angle created by tangent rays and chord

=> ∠ABC = 1/2.∠AOB = 1/2.2x = x

ΔOBC has OB = OC (are both radii)

=> ΔOBC is the  isosceles triangle at O

=> ∠OCB = (180° - ∠COB)/2 = (180° - 2x)/2 = 90° - x

because ∠OCB is the outer angle of ΔABC

=> ∠OCB = ∠ABC + ∠CAB

⇔ 90° - x = x + x

⇔ 90 = 3x

⇔ x = 30

Step-by-step explanation:

Answer:

Step-by-step explanation:

4+6+7+7+11+12+15+18+20= 100

divide by the number of values we have. we have 9 values

100/9=11.1111111111

I hope this helped

at first add all the number and divide it by how many numbers are there

4+6+7+7+11+12+15+18+20

= 100

now

divide

100÷ 9

11.1

Answer:

Step-by-step explanation: i thibnk 13

yeah i think its 13

Answer:

za=24

Step-by-step explanation:

supplementary angles add up to equal 180

180=7x+x+30+6

step 1 combine like terms

180=8x+36

step 2 subtract 36 from each side

144=8x

step 3 divide each side by 8

x=18

now we just plug in 18 to x in x+6

18+6=24

Answer:

24°

Step-by-step explanation:

The sum of supplementary angles is 180°.

Thus, we can set up our equation as:

(x + 6) + (7x + 30) = 180

Combine like terms.

8x + 36 = 180

Isolate the variable by subtracting 36 from both sides.

8x = 144

Divide both sides by 8.

x = 18

Now, let's revisit the equation for m∠ZA, and plug in our x.

((18) + 6)°

24°

Answer:

5

Step-by-step explanation:

(I'm assuming that by m2 and n2 you mean m to the power of 2 and n to the power of 2)

Whenever you have a number to a power, it is the same as that number times itself that power number of times. For example, 3 to the power of 4 is equal to 3 times itself 4 times, which is 3 * 3 * 3 * 3. If we use this and substitute the values in for m and n, we get that 3^2 - 2^2, and since 3^2 is 3 * 3 and 2^2 is 2 * 2 and 3 times 3 is 9 and 2 times 2 is 4, we get that 9 - 4 is 5.

Note: This symbol means to the power of ----> ^

Answer:

414

Step-by-step explanation:

10+4+400=414

Answer:

414

Step-by-step explanation:

Answer: -7x-7

Step-by-step explanation: Subtract 11 from 4

-7x-7

[tex]\text{Hey there!}[/tex]

[tex]\bold{-7x+4-11}\\\bold{COMBINE\ your\ LIKE\ TERMS}\\\bold{\-7x+ \underline{4}- \underline{11}}\\\bold{4-11=-7}\\\bold{7=7}\\\bold{=7x-7}\\\boxed{\boxed{\bold{Answer: -7x -7}}}\huge\checkmark[/tex]

[tex]\bf{Good\ luck\ on\ your\ assignment\ and\ enjoy\ your\ day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

y=-2/11x-7/11

Step-by-step explanation:

Answer:

[tex](-10,8)[/tex] or [tex]\frac{-10}{8}[/tex]

Step-by-step explanation:

In order to find the answer to this question you must put the coordinates into the slope formula and solve.

[tex]slope=\frac{y^2-y^1}{x^2-x^1}[/tex]

[tex](x^1,x^2)=(-1,-9)[/tex]

[tex](y^2-y^1)=(-3,7)[/tex]

Substitute:

[tex]\frac{-3-7}{-1--9}[/tex]

Solve using KCC:

[tex]-3-7=-3+-7=-10[/tex]

[tex]-1--9=-1+9=8[/tex]

[tex]slope=(-10,8)[/tex]

Hope this helps.